Group 8T1
Name 8T1 = C(8) Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8) Test Polynomials X^8+8*X^6+20*X^4+16*X^2+2, X^8-X^7-7*X^6+6*X^5+15*X^4-10*X^3-10*X^2+4*X+1

Group 8T2
Name 8T2 = 4[x]2 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,2,3,8)(4,5,6,7) Test Polynomials X^8+2*X^6+4*X^4+8*X^2+16, X^8-7*X^6+14*X^4-8*X^2+1, X^8-X^7+X^5-X^4+X^3-X+1

Group 8T3
Name 8T3 = E(8) Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7) Test Polynomials X^8-X^4+1, X^8-12*X^6+23*X^4-12*X^2+1

Group 8T4
Name 8T4 = D_8(8) Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (7,8)(1,6)(2,5)(3,4) Test Polynomials X^8-4*X^6+37*X^4-66*X^2+64, X^8-3*X^7+4*X^6-3*X^5+3*X^4-3*X^3+4*X^2-3*X+1, X^8+X^7-16*X^6+9*X^5+29*X^4-9*X^3-16*X^2-X+1

Group 8T5
Name 8T5 = Q_8(8) Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (4,2,6,8)(1,7,3,5) Test Polynomials X^8+12*X^6+36*X^4+36*X^2+9, X^8-12*X^6+36*X^4-36*X^2+9

Group 8T6
Name 8T6 = D(8) Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (7,8)(1,6)(2,5)(3,4) Test Polynomials X^8-3*X^5-X^4+3*X^3+1, X^8-X^7+X^5-2*X^4-X^3+2*X^2+2*X-1, X^8-4*X^7+6*X^6-7*X^5+8*X^4+5*X^3+27*X^2+26*X+19, X^8-2*X^7-9*X^6+10*X^5+22*X^4-14*X^3-15*X^2+2*X+1

Group 8T7
Name 8T7 = 1/2[2^3]4 Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (1,5)(3,7) Test Polynomials X^8+10*X^6+25*X^4+20*X^2+5, X^8-10*X^6+25*X^4-20*X^2+5, X^8-3*X^7-2*X^6+9*X^5-6*X^3-2*X^2-3*X+1

Group 8T8
Name 8T8 = 2D_8(8) Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (1,3)(2,6)(5,7) Test Polynomials X^8+24*X^6+126*X^4+216*X^2+117, X^8-2*X^7+2*X^6+X^4+5*X^3-7*X^2-6*X+1, X^8-14*X^6-10*X^5+31*X^4+15*X^3-14*X^2-5*X+1

Group 8T9
Name 8T9 = E(8):2 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (4,5)(6,7) Test Polynomials X^8+2*X^4-3*X^2+1, X^8-2*X^6-2*X^4-2*X^2+1, X^8-4*X^7+8*X^6-8*X^5+7*X^4+6*X^2+4*X+2, X^8-10*X^6-4*X^5+21*X^4+8*X^3-12*X^2-4*X+1, X^8-4*X^7+8*X^6-8*X^5+X^4+4*X^3-2*X^2+1, X^8+2*X^7+11*X^6+6*X^5+15*X^4+4*X^3+14*X^2-8*X+4

Group 8T10
Name 8T10 = [2^2]4 Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (1,5)(3,7) Test Polynomials X^8-13*X^6+44*X^4-17*X^2+1, X^8+X^7+8*X^6+11*X^4+2*X^2+7*X+31, X^8+3*X^7+5*X^6+3*X^5+4*X^4-3*X^3+5*X^2-3*X+1, X^8-2*X^7+X^6-X^5+4*X^4-3*X^3-X^2+X+1, X^8-2*X^7-4*X^6+4*X^5-X^4-8*X^3+4*X^2+6*X+1

Group 8T11
Name 8T11 = 1/2[2^3]E(4) Order 8 Soluble yes Primitive no Generators (1,5)(3,7), (2,4,6,8)(1,3,5,7), (1,4,5,8)(2,3,6,7) Test Polynomials X^8-X^5-2*X^4+4*X^2+X+1, X^8-2*X^7-X^6-5*X^4-X^2-2*X+1, X^8-2*X^7-7*X^6+16*X^5+4*X^4-18*X^3+2*X^2+4*X-1, X^8-2*X^7+5*X^6-16*X^5+25*X^4-28*X^3+59*X^2-14*X+49

Group 8T12
Name 8T12 = 2A_4(8) Order 8 Soluble yes Primitive no Generators (2,4,6,8)(1,3,5,7), (1,3,8)(4,5,7) Test Polynomials X^8-2*X^7+X^6+X^5-X^4+2*X^3+4*X^2-16*X+16, X^8-3*X^7-8*X^6+24*X^5+9*X^4-34*X^3-4*X^2+11*X-1

Group 8T13
Name 8T13 = E(8):3 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5) Test Polynomials X^8-3*X^6+3*X^4+2*X^2+1, X^8-2*X^7+4*X^4-4*X^3+4*X^2+2, X^8-3*X^7+X^6+7*X^5+8*X^4-16*X^3+9*X^2+8*X+13, X^8-4*X^7-6*X^6+24*X^5+13*X^4-28*X^3-12*X^2+4*X+1

Group 8T14
Name 8T14 = 1/2(S_4[x]2) Order 8 Soluble yes Primitive no Generators (2,8)(1,3)(4,6)(5,7), (1,2,3)(5,6,7), (1,4)(2,6)(3,7)(5,8) Test Polynomials X^8-26*X^6+99*X^4-126*X^2+49, X^8+4*X^6-4*X^5+11*X^4-8*X^3+18*X^2-14*X+3, X^8-8*X^7+35*X^6-98*X^5+193*X^4-268*X^3+257*X^2-154*X+43

Group 8T15
Name 8T15 = [1/4cD(4)^2]2 Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (7,8)(1,6)(2,5)(3,4), (1,5)(3,7) Test Polynomials X^8-X^4-1, X^8+12*X^6+45*X^4+54*X^2+19, X^8-4*X^7+2*X^6-4*X^5+12*X^4+12*X^3-4*X-2, X^8-2*X^7+3*X^6-2*X^5-X^4+6*X^3+7*X^2+4*X+1, X^8-X^7-11*X^6+4*X^5+21*X^4-4*X^3-11*X^2+X+1

Group 8T16
Name 8T16 = 1/2[2^4]4 Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (2,6)(3,7) Test Polynomials X^8-2*X^7-2*X^6+X^5+5*X^4+X^3+3*X^2+3*X+1, X^8-2*X^7-2*X^6+6*X^5-10*X^4+6*X^3-2*X^2-2*X+1, X^8-3*X^7-17*X^6+54*X^5+60*X^4-201*X^3-77*X^2+177*X+1, X^8-2*X^7-2*X^6+36*X^5-140*X^4+316*X^3-412*X^2+168*X+76, X^8-4*X^7+37*X^6-97*X^5+295*X^4-433*X^3+622*X^2-421*X+241

Group 8T17
Name 8T17 = [4^2]2 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,2,3,8) Test Polynomials X^8+12*X^6+48*X^4+68*X^2+17, X^8-2*X^7+3*X^6-4*X^4+4*X^3-2*X+1, X^8-X^6-6*X^5+3*X^3+X^2+2*X-1, X^8-4*X^7+14*X^5-8*X^4-12*X^3+7*X^2+2*X-1

Group 8T18
Name 8T18 = E(8):E_4 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (4,5)(6,7), (4,6)(5,7) Test Polynomials X^8+3*X^6+3*X^4+3*X^2+1, X^8-3*X^6+3*X^4-3*X^2+1, X^8+X^6+17*X^4+9*X^2+81, X^8-15*X^6+57*X^4-15*X^2+1, X^8-X^7-X^6+5*X^5+4*X^4+X^3-X^2-2*X+1

Group 8T19
Name 8T19 = [1/4eD(4)^2]2 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,3)(4,5,6,7) Test Polynomials X^8+X^6+2*X^2+4, X^8+4*X^4-4*X^2+1, X^8+14*X^6+36*X^4+28*X^2+4, X^8-14*X^6+36*X^4-28*X^2+4, X^8-2*X^7+12*X^6-13*X^5+24*X^4-13*X^3+12*X^2-2*X+1, X^8+2*X^7-7*X^6-14*X^5+22*X^4+66*X^3+15*X^2-90*X-63

Group 8T20
Name 8T20 = [2^3]4 Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (2,6)(3,7) Test Polynomials X^8-4*X^6-6*X^4+4*X^2+1, X^8+12*X^6+8*X^5+44*X^4-8*X^3+40*X^2-32*X+62, X^8-3*X^7+X^6-4*X^5-X^4-2*X^3-6*X^2+4*X+1, X^8-2*X^7+X^6+4*X^5+4*X^4-8*X^3+4*X^2+16*X+11, X^8+2*X^7-15*X^6+2*X^5+29*X^4-2*X^3-15*X^2-2*X+1

Group 8T21
Name 8T21 = [1/4dD(4)^2]2 Order 8 Soluble yes Primitive no Generators (2,8)(1,3)(4,6)(5,7), (1,5)(3,7), (1,4,5,8)(2,3)(6,7) Test Polynomials X^8+2*X^4-4*X^2+2, X^8+14*X^6+39*X^4+32*X^2+8, X^8-14*X^6+39*X^4-32*X^2+8, X^8-2*X^7-17*X^6-16*X^5-4*X^3-2*X^2+4, X^8-4*X^7+21*X^6-49*X^5+94*X^4-111*X^3+63*X^2-15*X+1

Group 8T22
Name 8T22 = E(8):D_4 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (2,3)(4,5), (2,3)(6,7) Test Polynomials X^8+13*X^6+47*X^4+44*X^2+4, X^8-2*X^6-8*X^5-5*X^4+8*X^3+12*X^2+4*X-1, X^8-18*X^6+8*X^5+79*X^4-32*X^3-96*X^2+32*X+1, X^8+6*X^7+18*X^6+28*X^5+19*X^4-12*X^3-26*X^2-10*X+13

Group 8T23
Name 8T23 = 2S_4(8) Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (1,3,8)(4,5,7) Test Polynomials X^8+X^7-3*X^6+X^5+8*X^4+X^2+7*X+1, X^8-X^7-X^5+25*X^4-54*X^3+50*X^2-8*X+9, X^8-4*X^7-4*X^6+26*X^5+2*X^4-52*X^3+31*X+1

Group 8T24
Name 8T24 = E(8):D_6 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5), (2,3)(4,5) Test Polynomials X^8-X^7+X^6+X^2+X+1, X^8-X^7+X^6-X^4+2*X^3+1, X^8+X^6-2*X^5+X^4-2*X^3+X^2+1, X^8-4*X^6-X^5+3*X^4+2*X^3+X^2-2*X-1, X^8-12*X^6-4*X^5+23*X^4+4*X^3-13*X^2+X+1, X^8-3*X^7+2*X^6+6*X^5-15*X^4+12*X^3+8*X^2-24*X+16

Group 8T25
Name 8T25 = F_56(8) Order 8 Soluble yes Primitive yes Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,6,3,4,5,7) Test Polynomials X^8-4*X^7+8*X^6-6*X^5+2*X^4+6*X^3-3*X^2+X+3, X^8-2*X^7-20*X^6+10*X^5+102*X^4+26*X^3-112*X^2-50*X+7

Group 8T26

Name 8T26 = 1/2[2^4]eD(4) Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (4,8)(1,5), (4,8)(1,7)(3,5) Test Polynomials X^8-5*X^5-3*X^4-5*X^3+1, X^8+3*X^6-3*X^5+3*X^4+6*X^2+6*X+3, X^8-4*X^7+4*X^6-X^4+4*X^2-4*X+1, X^8-2*X^7+X^6+2*X^5-2*X^4-2*X^3+X^2+2*X+1, X^8+X^7-11*X^6-8*X^5+38*X^4+21*X^3-39*X^2-23*X+1, X^8+2*X^7+20*X^6+37*X^5+164*X^4+233*X^3+615*X^2+518*X+811, X^8+2*X^7-14*X^6-60*X^5-246*X^4-906*X^3-1065*X^2+1880*X+4159

Group 8T27

Name 8T27 = [2^4]4 Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (4,8) Test Polynomials X^8-2*X^7+3*X^5-X^4-3*X^3+2*X+1, X^8-X^7-2*X^6+X^4-5*X^3-3*X^2+3*X+1, X^8-3*X^7+2*X^5+4*X^4+3*X^3-5*X^2-2*X+1, X^8+7*X^6-10*X^5+24*X^4-40*X^3+63*X^2-70*X+41, X^8-4*X^7+2*X^6+8*X^5-15*X^4+8*X^3+2*X^2-4*X+1, X^8+3*X^7+7*X^6+5*X^5+11*X^4+10*X^3+3*X^2+4*X+1, X^8-4*X^7-X^6+17*X^5-6*X^4-21*X^3+6*X^2+8*X+1

Group 8T28
Name 8T28 = 1/2[2^4]dD(4) Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (2,6)(3,7), (1,3)(5,7) Test Polynomials X^8-2*X^6+3*X^4+2, X^8+9*X^6+24*X^4+20*X^2+5, X^8-9*X^6+24*X^4-20*X^2+5, X^8-3*X^7+5*X^6-5*X^5+6*X^4-5*X^3+5*X^2-3*X+1, X^8-3*X^7+X^6+2*X^5-X^4+2*X^3+X^2-3*X+1, X^8-2*X^7-2*X^6+5*X^5+X^4-5*X^3-2*X^2+2*X+1, X^8-2*X^7-X^6+2*X^5-4*X^4+18*X^3-15*X^2-2*X+1

Group 8T29

Name 8T29 = E(8):D_8 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,3)(4,5,6,7), (1,3)(5,7) Test Polynomials X^8-X^6-X^4+X^2+1, X^8-9*X^6+25*X^4-22*X^2+4, X^8+12*X^6+42*X^4+36*X^2+4, X^8-2*X^7-2*X^5+6*X^3-3*X^2-2*X+1, X^8-2*X^7-2*X^6+8*X^4-2*X^3-5*X^2+4*X-1, X^8-2*X^7+5*X^6-3*X^5+6*X^4-X^3+5*X^2-X+1, X^8-X^7-3*X^6+3*X^5-2*X^4+9*X^3-7*X^2-2*X+1, X^8+2*X^7+X^6-4*X^5-5*X^4+4*X^3+14*X^2+12*X+4

Group 8T30
Name 8T30 = 1/2[2^4]cD(4) Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (2,6)(3,7), (1,3)(4,8)(5,7) Test Polynomials X^8-4*X^6-20*X^4+14, X^8+12*X^6+44*X^4+56*X^2+14, X^8-3*X^7+2*X^6+4*X^5-X^4-4*X^3+2*X^2+3*X+1, X^8-X^7+2*X^6-5*X^5+X^4-5*X^3+2*X^2-X+1, X^8+3*X^7-3*X^6-30*X^5-59*X^4-50*X^3-12*X^2+4*X+1, X^8-4*X^7-4*X^6+26*X^5-X^4-46*X^3+13*X^2+15*X+1

Group 8T31
Name 8T31 = [2^4]E(4) Order 8 Soluble yes Primitive no Generators (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (4,8) Test Polynomials X^8+12*X^6+48*X^4+72*X^2+31, X^8-8*X^5+X^4+12*X^3-2*X^2-4*X+1, X^8-2*X^7+X^6-6*X^5+6*X^3-X^2-2*X-1, X^8-2*X^7+X^6+2*X^5-3*X^4-2*X^3+X^2+2*X+1, X^8-2*X^7-3*X^6+8*X^5+3*X^4-16*X^3+3*X^2+6*X+1, X^8-4*X^7-4*X^6+18*X^5+8*X^4-20*X^3-3*X^2+6*X-1

Group 8T32
Name 8T32 = [2^3]A(4) Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5), (2,5)(3,4) Test Polynomials X^8-2*X^6-13*X^4-9*X^2+4, X^8-6*X^6+15*X^4-13*X^2+4, X^8+23*X^6+185*X^4+610*X^2+676, X^8+X^7-18*X^6+3*X^5+96*X^4-98*X^3-73*X^2+124*X-35

Group 8T33

Name 8T33 = [1/3A(4)^2]2 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5), (4,6)(5,7) Test Polynomials X^8-2*X^7-4*X^5+12*X^4+2*X^3-14*X^2-5*X+11, X^8-3*X^7-3*X^6+17*X^5-3*X^4-27*X^3+10*X^2+9*X+3, X^8-3*X^7-X^6+9*X^5-11*X^4+11*X^3-13*X^2+21*X-9, X^8-3*X^7+7*X^6-22*X^5+36*X^4-49*X^3+76*X^2-60*X+25, X^8-X^7-15*X^6+15*X^5+62*X^4-72*X^3-53*X^2+78*X-19

Group 8T34
Name 8T34 = 1/2[E(4)^2:S_3]2 Order 8 Soluble yes Primitive no Generators (1,2,3)(5,6,7), (4,8)(1,5)(2,7)(3,6), (1,8)(2,3) Test Polynomials X^8+6*X^6-4*X^5-31*X^4-12*X^3+96*X^2-26*X+29, X^8-X^7-6*X^6+13*X^5-6*X^4+X^3-14*X^2+7*X+1, X^8+6*X^7+12*X^6+10*X^5+24*X^4+42*X^3+40*X^2+18*X+3, X^8-X^7-28*X^6-13*X^5+202*X^4+277*X^3-100*X^2-203*X-11

Group 8T35

Name 8T35 = [2^4]D(4) Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (1,3)(5,7), (4,8) Test Polynomials X^8+2*X^6-12*X^4-3*X^2+11, X^8+11*X^6+42*X^4+64*X^2+31, X^8-3*X^7+5*X^6-5*X^5+3*X^4-X+1, X^8-X^7-2*X^5+3*X^4+2*X^3+X+1, X^8-X^7-2*X^6+2*X^4+2*X^3-X^2-X-1, X^8-X^7-3*X^6+5*X^5+3*X^4-11*X^3+8*X-1, X^8-X^7+X^6-2*X^5+3*X^4-4*X^3+4*X^2-2*X+1, X^8-X^7+X^6-2*X^5+X^4-2*X^3+X^2-X+1, X^8-X^7-X^6-2*X^5+3*X^4+4*X^3-4*X^2-2*X+1, X^8-2*X^7-2*X^6+X^5+X^4+5*X^3-X^2-3*X+1, X^8-3*X^7-5*X^6+14*X^5+8*X^4-16*X^3-2*X^2+5*X-1

Group 8T36
Name 8T36 = E(8):F_21 Order 8 Soluble yes Primitive yes Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5), (1,2,6,3,4,5,7) Test Polynomials X^8+3*X^7+20*X^4+18*X^3-18*X^2-8*X+14, X^8-2*X^7-22*X^6+50*X^5+72*X^4-256*X^3+180*X^2-12*X-10

Group 8T37
Name 8T37 = L(8) Order 8 Soluble no Primitive yes Generators (1,2,4)(3,6,5), (7,8)(1,6)(2,3)(4,5), (1,2,3,4,5,6,8) Test Polynomials X^8-4*X^7+7*X^6-7*X^5+7*X^4-7*X^3+7*X^2+5*X+1, X^8-2*X^7-38*X^6+16*X^5+436*X^4+424*X^3-560*X^2-488*X-28

Group 8T38
Name 8T38 = [2^4]A(4) Order 8 Soluble yes Primitive no Generators (1,8)(2,3)(4,5)(6,7), (1,2,3)(5,6,7), (4,8) Test Polynomials X^8-2*X^6-7*X^4+3*X^2+8, X^8-7*X^6+11*X^4+6*X^2-7, X^8+14*X^6+29*X^4+17*X^2+3, X^8-2*X^7+2*X^6+X^4+2*X^2+2*X+1, X^8-X^7-3*X^6-X^5+X^4-X^3-3*X^2-X+1, X^8-3*X^7-13*X^6+18*X^5+42*X^4-17*X^3-31*X^2+2*X+4

Group 8T39

Name 8T39 = [2^3]S(4) Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5), (1,6)(2,3,5,4) Test Polynomials X^8+X^4+X^2+1, X^8+X^4-4*X^2+1, X^8-X^7+X^6+X^5-2*X^4+X^3+X^2-X+1, X^8-4*X^7+6*X^6-4*X^5-4*X^4+10*X^3-3*X^2-2*X+1, X^8-X^7-11*X^6+X^5+24*X^4+X^3-11*X^2-X+1, X^8-2*X^7+139*X^6-94*X^5+6348*X^4+5782*X^3+97492*X^2+262652*X+294463

Group 8T40
Name 8T40 = 1/2[2^4]S(4) Order 8 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8), (1,8)(2,3)(4,5)(6,7), (1,2,3)(5,6,7), (4,8)(1,5), (2,3)(4,8)(6,7) Test Polynomials X^8-X^7+4*X^5-2*X^4+3*X^2-X+1, X^8-X^7-4*X^5+2*X^4+3*X^2-X-1, X^8+4*X^7+9*X^6+13*X^5+X^4-15*X^3-14*X^2-5*X+7, X^8+4*X^7-2*X^6-20*X^5-10*X^4+18*X^3+10*X^2-3*X-1, X^8+4*X^7+34*X^6+88*X^5+280*X^4+418*X^3+586*X^2+391*X+142

Group 8T41

Name 8T41 = [E(4)^2:S_3]2 Order 8 Soluble yes Primitive no Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5), (1,3)(4,5,6,7) Test Polynomials X^8-2*X^6-4*X^5+4*X^3-10*X^2-8*X-1, X^8+2*X^6+15*X^4-24*X^3-10*X^2+24*X+13, X^8-4*X^7+5*X^6-X^4-4*X^3+X^2+2*X+1, X^8-14*X^6+4*X^5+36*X^4-4*X^3-22*X^2+4*X+2, X^8-3*X^7+4*X^6-4*X^5+6*X^4-6*X^3+4*X^2-2*X+1, X^8-3*X^7+4*X^6+11*X^5-19*X^4-X^3+14*X^2-7*X+1, X^8-2*X^7-59*X^6+1440*X^5+7704*X^4-37440*X^3+1241568*X^2+18247680*X+62042112

Group 8T42
Name 8T42 = [A(4)^2]2 Order 8 Soluble yes Primitive no Generators (1,2,3), (4,8)(1,5)(2,6)(3,7), (2,8)(1,3) Test Polynomials X^8-2*X^7+2*X^6-2*X^5+2*X^4-X+1, X^8-4*X^7+2*X^6+6*X^5+X^4-10*X^3+4*X+1, X^8-X^7-X^6-2*X^5-X^4+X^3-4*X^2+7*X+1, X^8+4*X^7-8*X^6-28*X^5+17*X^4+42*X^3-20*X^2-18*X+9

Group 8T43
Name 8T43 = L(8):2 Order 8 Soluble no Primitive yes Generators (1,3,2,6,4,5), (7,8)(1,6)(2,3)(4,5), (1,2,3,4,5,6,8) Test Polynomials X^8-X^6-3*X^5-X^4+4*X^3+4*X^2-2*X-1, X^8-X^7+3*X^6-3*X^5+2*X^4-2*X^3+5*X^2+5*X+1, X^8-2*X^7-35*X^6+308*X^4+308*X^3-462*X^2-556*X+6

Group 8T44
Name 8T44 = [2^4]S(4) Order 8 Soluble yes Primitive no Generators (1,2,3,8)(4,5,6,7), (1,8)(4,5), (4,8) Test Polynomials X^8-X^5-X^4-X^3+1, X^8+X^6-4*X^4-X^2+2, X^8+12*X^6+50*X^4+83*X^2+43, X^8-X^7-X^5+2*X^3+X-1, X^8-X^7-X^6+X^4-X^2+X+1, X^8-X^7+X^4+2*X^3-2*X^2-X+1, X^8-X^7+X^5-8*X^4+X^3+8*X^2-2*X-1, X^8-2*X^7-X^6+5*X^5-2*X^4-6*X^3+3*X^2+2*X-1, X^8-4*X^7-X^6+15*X^5-3*X^4-16*X^3+4*X^2+4*X-1

Group 8T45
Name 8T45 = [1/2S(4)^2]2 Order 8 Soluble yes Primitive no Generators (1,2,3), (4,8)(1,5)(2,6)(3,7), (1,8)(4,5), (2,8)(1,3) Test Polynomials X^8-2*X^6+7*X^4-8*X^2-4*X+7, X^8-2*X^6+X^4+4*X^2-4*X+1, X^8-6*X^6-6*X^5+X^4+2*X^3+7*X^2+8*X-8, X^8-X^7-4*X^6+4*X^5+7*X^4-8*X^3-4*X^2+5*X-1, X^8-X^7-11*X^6+8*X^5+40*X^4-17*X^3-54*X^2+6*X+19

Group 8T46
Name 8T46 = 1/2[S(4)^2]2 Order 8 Soluble yes Primitive no Generators (1,2,3), (1,8)(4,5), (2,8)(1,3), (4,8)(1,5)(2,7,3,6) Test Polynomials X^8-X^7+X^5-4*X^4+5*X^3+6*X^2-2*X-1, X^8+2*X^7+7*X^6+11*X^5+19*X^4+20*X^3+20*X^2+10*X+5, X^8+7*X^7-10*X^6-131*X^5-200*X^4+131*X^3+382*X^2-191, X^8+X^7-40*X^6+44*X^5+4*X^4+400*X^3-320*X^2+1920*X-2048

Group 8T47
Name 8T47 = [S(4)^2]2 Order 8 Soluble yes Primitive no Generators (2,3), (4,8)(1,5)(2,6)(3,7), (1,2,3,8) Test Polynomials X^8-2*X^7+2*X^6+X^3+X+1, X^8-2*X^5+X^4+3*X^3-2*X^2-X+1, X^8-2*X^6-3*X^5+3*X^3+2*X^2-X-1, X^8-X^7+X^5-2*X^3-2*X^2+X+1, X^8-3*X^7+2*X^5+14*X^4-22*X^3+8*X+1, X^8-X^7-3*X^6+4*X^5-2*X^4-X^3+5*X^2-X-1, X^8-X^7-7*X^6+5*X^5+15*X^4-7*X^3-10*X^2+2*X+1

Group 8T48
Name 8T48 = AL(8) Order 8 Soluble no Primitive yes Generators (4,8)(1,5)(2,6)(3,7), (1,8)(2,3)(4,5)(6,7), (2,8)(1,3)(4,6)(5,7), (1,2,3)(4,6,5), (1,2,6,3,4,5,7), (1,2)(5,6) Test Polynomials X^8+3*X^7-X^6-10*X^5-9*X^4-X^3+7*X^2+11*X+4, X^8-4*X^7+8*X^6-11*X^5+12*X^4-10*X^3+6*X^2-3*X+2, X^8+4*X^7-10*X^6-48*X^5-24*X^4+36*X^3+14*X^2-8*X-1, X^8-3*X^7+10*X^6-17*X^5+26*X^4-29*X^3+26*X^2-19*X+9

Group 8T49
Name 8T49 = A(8) Order 8 Soluble no Primitive yes Generators (4,5,8), (5,6,8), (3,4,8), (6,7,8), (1,2,8), (2,3,8) Test Polynomials X^8-2*X^7+3*X^5-5*X^4+2*X^3+2*X^2-X+1, X^8-3*X^7+3*X^6-X^5+2*X^4-3*X^3+2*X^2-X+1, X^8-2*X^7-11*X^6+6*X^5+30*X^4-2*X^3-22*X^2+X+3

Group 8T50
Name 8T50 = S(8) Order 8 Soluble no Primitive yes Generators (4,8), (2,8), (5,8), (6,8), (1,8), (3,8), (7,8) Test Polynomials X^8-X^6-X^5-3*X^4+4*X^2-1, X^8-3*X^7+3*X^6-2*X^4+3*X^3-X^2+X-1, X^8-X^7-7*X^6+4*X^5+15*X^4-3*X^3-9*X^2+1, X^8-X^7+2*X^6-3*X^5+3*X^4-3*X^3+3*X^2-2*X+1, X^8-2*X^7-X^6+X^5-2*X^4+4*X^3+3*X^2-2*X-1