Group 6T1
    Name6T1 = C(6)
    Order6
    Solubleyes
    Primitiveno
    Generators(1,2,3,4,5,6)
    Test PolynomialsX^6-X^5+X^4-X^3+X^2-X+1, X^6-X^5-7*X^4+2*X^3+7*X^2-2*X-1
    Group 6T2
    Name6T2 = D_6(6)
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6)(1,3,5), (5,6)(1,4)(2,3)
    Test PolynomialsX^6-3*X^5-2*X^4+9*X^3-5*X+1, X^6-3*X^5+5*X^4-5*X^3+5*X^2-3*X+1
    Group 6T3
    Name6T3 = S(3)[x]2
    Order6
    Solubleyes
    Primitiveno
    Generators(1,2,3,4,5,6), (5,6)(1,4)(2,3)
    Test PolynomialsX^6+X^4-2*X^3+X^2-X+1, X^6-3*X^5+X^4+10*X^2-9*X+3, X^6-X^5-X^4+4*X^3+3*X^2-1, X^6-X^5-10*X^4+X^3+12*X^2-3*X-1
    Group 6T4
    Name6T4 = A_4(6)
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6)(1,3,5), (1,4)(2,5)
    Test PolynomialsX^6+X^4-2*X^2-1, X^6-19*X^4+104*X^2-169
    Group 6T5
    Name6T5 = F_18(6)
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6), (3,6)(1,4)(2,5)
    Test PolynomialsX^6-3*X^5+4*X^4-2*X^3+X^2-X+1, X^6-X^5-6*X^4+7*X^3+4*X^2-5*X+1
    Group 6T6
    Name6T6 = 2A_4(6)
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6)(1,3,5), (3,6)
    Test PolynomialsX^6-2*X^5+2*X^3-X-1, X^6-X^5-X^4-2*X^3+2*X^2+3*X-1, X^6-2*X^5-4*X^4+5*X^3+4*X^2-2*X-1, X^6-2*X^5+5*X^4-7*X^3+10*X^2-8*X+8
    Group 6T7
    Name6T7 = [2^2]S(3)
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6)(1,3,5), (1,4)(2,5), (1,5)(2,4)
    Test PolynomialsX^6+X^4-1, X^6-6*X^4+8*X^2-1, X^6-X^4-X^3-X^2+1
    Group 6T8
    Name6T8 = 1/2[2^3]S(3)
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6)(1,3,5), (1,4)(2,5), (1,5)(2,4)(3,6)
    Test PolynomialsX^6+4*X^5-9*X^4-51*X^3-46*X^2+8, X^6-2*X^5+2*X^4-4*X^3+4*X^2-2*X+2, X^6-3*X^5+6*X^4-7*X^3+2*X^2+X-1
    Group 6T9
    Name6T9 = F_18(6):2
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6), (3,6)(1,4)(2,5), (1,5)(2,4)
    Test PolynomialsX^6-3*X^5+4*X^4-X^3+X^2-2*X+7, X^6-3*X^5+3*X^4-2*X^3-3*X^2+X-1, X^6-2*X^5-10*X^4+8*X^3+32*X^2+14*X+1
    Group 6T10
    Name6T10 = 1/2[S(3)^2]2
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6), (1,5)(2,4), (3,6)(1,4,5,2)
    Test PolynomialsX^6-X^5+X^4-X^3-4*X^2+5, X^6-21*X^4+21*X^3+99*X^2-198*X+99
    Group 6T11
    Name6T11 = [2^3]S(3)
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4,6)(1,3,5), (3,6), (1,5)(2,4)
    Test PolynomialsX^6-X^5-X^3-X+1, X^6-2*X^5+4*X^4-6*X^3+8*X^2-8*X+8, X^6-2*X^5+2*X^4-2*X^3+2*X^2-X+1, X^6-3*X^5+X^4+4*X^3-3*X^2-2*X+1, X^6-2*X^5-2*X^4+5*X^3-2*X^2-2*X+1, X^6-3*X^5-2*X^4+9*X^3-X^2-4*X+1
    Group 6T12
    Name6T12 = PSL(2,5)
    Order6
    Solubleno
    Primitiveyes
    Generators(1,2,3,4,6), (5,6)(1,4)
    Test PolynomialsX^6-10*X^4-7*X^3+15*X^2+14*X+3, X^6-2*X^5+3*X^4-4*X^3+2*X^2-2*X-1
    Group 6T13
    Name6T13 = F_36(6):2
    Order6
    Solubleyes
    Primitiveno
    Generators(2,4), (2,4,6), (3,6)(1,4)(2,5)
    Test PolynomialsX^6-2*X^5+2*X^4-X+1, X^6-X^5+2*X^4-X^2+X-1, X^6-X^5-2*X^4-X^3+X^2+2*X-1, X^6-3*X^5-2*X^4+10*X^3-X^2-7*X+1
    Group 6T14
    Name6T14 = PGL(2,5)
    Order6
    Solubleno
    Primitiveyes
    Generators(1,2,3,4,6), (1,2)(3,4)(5,6)
    Test PolynomialsX^6+3*X^4-2*X^3+6*X^2+1, X^6-18*X^4+9*X^3+90*X^2-70*X-69, X^6-2*X^5-X^4+4*X^3-4*X^2+4*X+1
    Group 6T15
    Name6T15 = A(6)
    Order6
    Solubleno
    Primitiveyes
    Generators(1,2,6), (2,3,6), (3,4,6), (4,5,6)
    Test PolynomialsX^6-2*X^4+X^2-2*X-1, X^6-3*X^5-9*X^4+14*X^3+27*X^2-3*X-10
    Group 6T16
    Name6T16 = S(6)
    Order6
    Solubleno
    Primitiveyes
    Generators(3,6), (1,6), (2,6), (4,6), (5,6)
    Test PolynomialsX^6-X^5+X^3-X^2+1, X^6-X^5+X^4-X^2+2*X-1, X^6-X^5-2*X^4+3*X^3-X^2-2*X+1, X^6-X^5-5*X^4+4*X^3+5*X^2-2*X-1