Group 9T1
Name 9T1 = C(9) Order 9 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8,9) Test Polynomials X^9-X^8-8*X^7+7*X^6+21*X^5-15*X^4-20*X^3+10*X^2+5*X-1

Group 9T2
Name 9T2 = 3[x]3 Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8) Test Polynomials X^9-15*X^7-4*X^6+54*X^5+12*X^4-38*X^3-9*X^2+6*X+1

Group 9T3
Name 9T3 = D(9) Order 9 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8,9), (1,8)(2,7)(3,6)(4,5) Test Polynomials X^9-3*X^8+4*X^7-5*X^6+6*X^5-X^4-5*X^3+4*X^2-2, X^9+X^8-16*X^7+6*X^6+64*X^5-65*X^4-48*X^3+78*X^2-19*X-1

Group 9T4
Name 9T4 = S(3)[x]3 Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,2)(4,5)(7,8) Test Polynomials X^9-5*X^8-X^7+4*X^6+2*X^5+3*X^4-X^3-3*X^2+1, X^9-3*X^8-8*X^7+13*X^6+22*X^5-13*X^4-20*X^3+X^2+5*X+1

Group 9T5
Name 9T5 = S(3)[1/2]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,2)(3,6)(4,8)(5,7) Test Polynomials X^9-3*X^6+3*X^3+1, X^9-54*X^7-12*X^6+756*X^5+180*X^4-2652*X^3-864*X^2+288*X+64

Group 9T6
Name 9T6 = 1/3[3^3]3 Order 9 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8,9), (1,4,7)(2,8,5) Test Polynomials X^9-3*X^8-10*X^7+42*X^6-28*X^5-28*X^4+28*X^3+2*X^2-6*X+1

Group 9T7
Name 9T7 = [3^2]3 Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (3,4,5)(6,8,7) Test Polynomials X^9-3*X^8-21*X^7+78*X^5+69*X^4-21*X^3-39*X^2-12*X-1

Group 9T8
Name 9T8 = S(3)[x]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,2)(4,5)(7,8), (3,6)(4,7)(5,8) Test Polynomials X^9-X^8+3*X^6+X^5+X^4+3*X^3+2*X^2+1, X^9-16*X^7-7*X^6+48*X^5+20*X^4-37*X^3-16*X^2+4*X+1, X^9-2*X^8-3*X^7+9*X^6-4*X^5-6*X^4+10*X^3-4*X^2-X-1

Group 9T9
Name 9T9 = E(9):4 Order 9 Soluble yes Primitive yes Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,8,2,4)(3,5,6,7) Test Polynomials X^9-45*X^7-93*X^6+72*X^5+216*X^4+63*X^3-81*X^2-54*X-9, X^9-2*X^8+8*X^7-8*X^6+20*X^5-8*X^4+4*X^3-24*X^2+23*X-6

Group 9T10
Name 9T10 = [3^2]S(3)_6 Order 9 Soluble yes Primitive no Generators (1,2,3,4,5,6,7,8,9), (1,8)(2,7)(3,6)(4,5), (1,4,7)(2,8,5) Test Polynomials X^9+6*X^8+15*X^7+18*X^6+11*X^5+X^4-2*X^3+3*X^2-X+1, X^9-4*X^8-14*X^7+44*X^6+62*X^5-120*X^4-92*X^3+48*X^2+12*X-4

Group 9T11
Name 9T11 = 1/2[3^2:2]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,2)(3,6)(4,8)(5,7), (3,4,5)(6,8,7) Test Polynomials X^9-3*X^6+3*X^3+8, X^9-27*X^7+30*X^6+189*X^5-378*X^4-21*X^3+378*X^2-126*X-42

Group 9T12
Name 9T12 = [3^2]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (3,4,5)(6,8,7), (3,6)(4,7)(5,8) Test Polynomials X^9-4*X^8+4*X^7+4*X^6-7*X^5-2*X^4+4*X^3+3*X^2-X-1, X^9-19*X^7-10*X^6+100*X^5+86*X^4-120*X^3-99*X^2+30*X+23

Group 9T13
Name 9T13 = [1/2S(3)^2]3 Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (3,4,5)(6,8,7), (1,2)(3,5)(6,7) Test Polynomials X^9-X^6-2*X^3+1, X^9-4*X^8-30*X^7+142*X^6+79*X^5-680*X^4-247*X^3+998*X^2+716*X+104

Group 9T14
Name 9T14 = E(9):Q_8 Order 9 Soluble yes Primitive yes Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,8,2,4)(3,5,6,7), (1,6,2,3)(4,7,8,5) Test Polynomials X^9-3*X^8+12*X^7-12*X^6+12*X^5-12*X^4+12*X^3-12*X^2+9*X-3, X^9-2*X^8-60*X^7+120*X^6+980*X^5-1808*X^4-4012*X^3+4936*X^2+4673*X-1434

Group 9T15
Name 9T15 = E(9):8 Order 9 Soluble yes Primitive yes Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,6,4,5,2,3,8,7) Test Polynomials X^9-9*X^7-21*X^6+72*X^5+99*X^4-99*X^3-585*X^2+549*X+166, X^9-72*X^7+1464*X^5-960*X^4-8928*X^3+13440*X^2-2064*X-2560

Group 9T16
Name 9T16 = E(9):D_8 Order 9 Soluble yes Primitive yes Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,2)(3,5)(6,7), (1,8)(2,4)(5,7) Test Polynomials X^9-X^8-2*X^6-X^5+3*X^4+X^2+X-1, X^9-10*X^7-3*X^6+25*X^5+5*X^4-21*X^3+5*X-1, X^9-2*X^8+2*X^7-X^6-X^5+X^4-X^3+X-1

Group 9T17
Name 9T17 = 3 wr 3 Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9) Test Polynomials X^9-4*X^8-2*X^7+22*X^6-14*X^5-22*X^4+20*X^3+2*X^2-5*X+1

Group 9T18
Name 9T18 = [1/2S(3)^2]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,2)(3,6)(4,8)(5,7), (3,4,5)(6,8,7), (1,2)(3,5)(6,7) Test Polynomials X^9-X^3-1, X^9-2*X^6-4*X^3+1, X^9-9*X^7-X^6+27*X^5+6*X^4-28*X^3-9*X^2+3*X-1, X^9-3*X^8-39*X^7+167*X^6-24*X^5-480*X^4+136*X^3+384*X^2+144*X+16

Group 9T19
Name 9T19 = E(9):2D_8 Order 9 Soluble yes Primitive yes Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (1,2)(3,5)(6,7), (1,6,4,5,2,3,8,7) Test Polynomials X^9-3*X^8+6*X^7-18*X^6+12*X^5-24*X^4+24*X^3-12*X^2+6*X-2, X^9-2*X^8-8*X^7+16*X^6+28*X^5-32*X^4-24*X^3+24*X^2+X-2, X^9-3*X^8-32*X^7+80*X^6+298*X^5-558*X^4-616*X^3+616*X^2+255*X-29

Group 9T20
Name 9T20 = [3^3]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (3,6)(4,7)(5,8), (1,2,9) Test Polynomials X^9-4*X^8+6*X^7-8*X^6+7*X^5-4*X^4+2*X^3+1, X^9-4*X^8-4*X^7+22*X^6-X^5-31*X^4+4*X^3+15*X^2-1

Group 9T21
Name 9T21 = 1/2[3^3:2]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2)(3,6)(4,8)(5,7), (1,2,9) Test Polynomials X^9-4*X^8+6*X^7-9*X^6+13*X^5+3*X^4-24*X^3+15*X^2-5*X+5, X^9+3*X^8-10*X^7-37*X^6+4*X^5+81*X^4+21*X^3-50*X^2-10*X+10

Group 9T22
Name 9T22 = [3^3:2]3 Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2)(4,5)(7,8), (1,2,9) Test Polynomials X^9-4*X^8+8*X^7-11*X^6+9*X^5-3*X^4+5*X^3-4*X^2-X+1, X^9-30*X^7-20*X^6+279*X^5+372*X^4-659*X^3-1566*X^2-1044*X-232

Group 9T23
Name 9T23 = E(9):2A_4 Order 9 Soluble yes Primitive yes Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (3,4,5)(6,8,7), (1,8,2,4)(3,5,6,7) Test Polynomials X^9-3*X^8+X^6+15*X^5-13*X^4-3*X^3+4*X-1, X^9+2*X^8-66*X^7-196*X^6+1022*X^5+3614*X^4-2711*X^3-14194*X^2-4931*X+5714

Group 9T24
Name 9T24 = [3^3:2]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2)(4,5)(7,8), (3,6)(4,7)(5,8), (1,2,9) Test Polynomials X^9+X^8+3*X^7+3*X^5-5*X^4+6*X^3+X+1, X^9+X^8-9*X^7-10*X^6+2*X^5+35*X^4+5*X^3-17*X^2-8*X-1, X^9-X^8-6*X^7+2*X^6+12*X^5+10*X^4-2*X^3-14*X^2-7*X-1, X^9-2*X^8-17*X^7+33*X^6+90*X^5-183*X^4-161*X^3+379*X^2+36*X-193

Group 9T25
Name 9T25 = [1/2S(3)^3]3 Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9), (4,5)(7,8) Test Polynomials X^9-3*X^8+3*X^7+4*X^6-12*X^5+9*X^4+X^3-9*X^2+6*X-1, X^9+3*X^8-20*X^7-63*X^6+87*X^5+355*X^4+147*X^3-313*X^2-317*X-83

Group 9T26
Name 9T26 = E(9):2S_4 Order 9 Soluble yes Primitive yes Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9)(3,4,5)(6,7,8), (3,4,5)(6,8,7), (1,6,4,5,2,3,8,7) Test Polynomials X^9-X^7-5*X^6+X^5+2*X^4+4*X^3-3*X^2-X+1, X^9-3*X^8-22*X^6-9*X^5-30*X^4+2*X^3+3*X^2+3*X-1, X^9-60*X^7-30*X^6+441*X^5+90*X^4-1116*X^3+180*X^2+972*X-480

Group 9T27
Name 9T27 = PSL(2,8) Order 9 Soluble no Primitive yes Generators (1,2,4,3,6,7,5), (1,9)(2,3)(4,5)(6,7), (8,9)(2,5)(3,6)(4,7) Test Polynomials X^9+X^7-4*X^6-12*X^4-X^3-7*X^2-X-1

Group 9T28
Name 9T28 = [S(3)^3]3 Order 9 Soluble yes Primitive no Generators (1,2), (3,6,9)(1,4,7)(2,5,8), (1,2,9) Test Polynomials X^9-2*X^8+3*X^7-X^6-2*X^5+5*X^4-4*X^3+2*X-1, X^9-11*X^7-4*X^6+31*X^5+13*X^4-24*X^3-11*X^2+3*X+1, X^9-2*X^8+X^7+2*X^6-5*X^5+2*X^4+X^3-3*X^2+X+1, X^9-2*X^8-5*X^7+12*X^6+3*X^5-19*X^4+7*X^3+7*X^2-2*X-1

Group 9T29
Name 9T29 = [1/2S(3)^3]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (3,6)(4,7)(5,8), (1,2,9), (4,5)(7,8) Test Polynomials X^9-3*X^6-5*X^5+5*X^2-1, X^9-X^8+3*X^6+3*X^4-X^3-2*X^2-3*X-1, X^9+3*X^8-7*X^7-21*X^6+17*X^5+42*X^4-21*X^3-22*X^2+14*X-2

Group 9T30
Name 9T30 = 1/2[S(3)^3]S(3) Order 9 Soluble yes Primitive no Generators (3,6,9)(1,4,7)(2,5,8), (1,2,9), (4,5)(7,8), (1,2)(3,6)(4,7)(5,8) Test Polynomials X^9-X^8+2*X^5-2*X^4+2*X^2-2*X+1, X^9-4*X^8-2*X^7+6*X^5+4*X^4-4*X^3+2*X^2-2, X^9-19*X^7-24*X^6+53*X^5+73*X^4-46*X^3-53*X^2+15*X+9

Group 9T31

Name 9T31 = [S(3)^3]S(3) Order 9 Soluble yes Primitive no Generators (1,2), (3,6,9)(1,4,7)(2,5,8), (3,6)(4,7)(5,8), (1,2,9) Test Polynomials X^9-5*X^7-X^6+7*X^5+4*X^4-2*X^3-5*X^2-X+1, X^9-6*X^7+X^6+7*X^5+7*X^4-11*X^3-X^2+4*X-1, X^9-3*X^8+X^7+4*X^6-4*X^5+X^4+X^3-X^2-1, X^9-3*X^8+4*X^7-5*X^6+6*X^5-6*X^4+5*X^3-4*X^2+2*X-1, X^9-X^8-9*X^7+6*X^6+22*X^5-9*X^4-17*X^3+5*X^2+4*X-1, X^9-4*X^8-X^7+17*X^6-5*X^5-24*X^4+6*X^3+13*X^2-X-1

Group 9T32
Name 9T32 = P|L(2,8) Order 9 Soluble no Primitive yes Generators (1,2,4,3,6,7,5), (1,9)(2,3)(4,5)(6,7), (8,9)(2,5)(3,6)(4,7), (2,4,6)(3,5,7) Test Polynomials X^9-X^8-4*X^7+28*X^3+26*X^2+9*X+1

Group 9T33
Name 9T33 = A(9) Order 9 Soluble no Primitive yes Generators (1,2,9), (2,3,9), (3,4,9), (4,5,9), (6,7,9), (7,8,9), (5,6,9) Test Polynomials X^9-X^8-X^7-2*X^5+4*X^4-5*X^2+1, X^9-3*X^8+5*X^7-7*X^6+5*X^5-3*X^3+6*X^2-4*X+1, X^9+X^8-17*X^7-35*X^6+18*X^5+69*X^4+8*X^3-33*X^2-3*X+4

Group 9T34
Name 9T34 = S(9) Order 9 Soluble no Primitive yes Generators (6,9), (7,9), (8,9), (3,9), (4,9), (5,9), (1,9), (2,9) Test Polynomials X^9-4*X^7+X^5-2*X^4+5*X^3+3*X^2-2*X-1, X^9-X^8-3*X^7+3*X^6+2*X^5-X^4-3*X^2+1, X^9-3*X^8+6*X^7-8*X^6+7*X^5-3*X^4+2*X^2-2*X+1, X^9-2*X^8+X^7+X^6-3*X^5+X^4+3*X^3-2*X-1, X^9-2*X^8-7*X^7+11*X^6+15*X^5-15*X^4-10*X^3+7*X^2+2*X-1