Group 7T1
Name
7T1 = C(7)
Order
7
Soluble
yes
Primitive
yes
Generators
(1,2,3,4,5,6,7)
Test Polynomials
X^7-X^6-12*X^5+7*X^4+28*X^3-14*X^2-9*X-1
Group 7T2
Name
7T2 = D(7)
Order
7
Soluble
yes
Primitive
yes
Generators
(1,2,3,4,5,6,7)
,
(1,6)(2,5)(3,4)
Test Polynomials
X^7-2*X^6+2*X^5+X^3-3*X^2+X-1, X^7-2*X^6-7*X^5+10*X^4+13*X^3-10*X^2-X+1
Group 7T3
Name
7T3 = F_21(7)
Order
7
Soluble
yes
Primitive
yes
Generators
(1,2,3,4,5,6,7)
,
(1,2,4)(3,6,5)
Test Polynomials
X^7-8*X^5-2*X^4+16*X^3+6*X^2-6*X-2
Group 7T4
Name
7T4 = F_42(7)
Order
7
Soluble
yes
Primitive
yes
Generators
(1,2,3,4,5,6,7)
,
(1,3,2,6,4,5)
Test Polynomials
X^7-3*X^6+9*X^5-13*X^4+17*X^3-10*X^2+4*X+1, X^7-X^6-12*X^5+9*X^4+37*X^3-26*X^2-21*X+5
Group 7T5
Name
7T5 = L(7)
Order
7
Soluble
no
Primitive
yes
Generators
(1,2,3,4,5,6,7)
,
(1,2)(3,6)
Test Polynomials
X^7-8*X^5-2*X^4+15*X^3+4*X^2-6*X-2, X^7-X^6-3*X^5+X^4+4*X^3-X^2-X+1
Group 7T6
Name
7T6 = A(7)
Order
7
Soluble
no
Primitive
yes
Generators
(1,2,7)
,
(2,3,7)
,
(3,4,7)
,
(4,5,7)
,
(5,6,7)
Test Polynomials
X^7-2*X^6+4*X^4-5*X^3+2*X-1, X^7-2*X^6-7*X^5+11*X^4+16*X^3-14*X^2-11*X+2
Group 7T7
Name
7T7 = S(7)
Order
7
Soluble
no
Primitive
yes
Generators
(1,7)
,
(2,7)
,
(3,7)
,
(4,7)
,
(5,7)
,
(6,7)
Test Polynomials
X^7-X^6-X^5+X^3+X^2-X-1, X^7-X^6+X^5-X^3+X^2-X-1, X^7-3*X^5-X^4+X^3+3*X^2+X-1, X^7-X^6-6*X^5+5*X^4+8*X^3-5*X^2-2*X+1