Galois Group: 10T42

• Label: 10T42
• Order: \(14400\)
• n: \(10\)
• Cyclic: No
• Abelian: No
• Solvable: No
• Primitive: No
• $p$-group: No
• Group: $A_5^2 : C_4$

Group action invariants

Degree $n$ :		$10$
Transitive number $t$ :		$42$
Group :		$A_5^2 : C_4$
CHM label :		$1/2[S(5)^{2}]2$
Parity:		$1$
Primitive:		No
Nilpotency class:		$-1$ (not nilpotent)
Generators:		(2,4,6,8,10), (1,6)(2,5,10,7)(3,8)(4,9)
$|\Aut(F/K)|$:		$1$

Low degree resolvents

|G/N|	Galois groups for stem field(s)
2:	$C_2$
4:	$C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 5: None

Low degree siblings

12T278, 20T457, 20T461, 24T12116, 25T100, 30T817, 36T9861, 40T10509, 40T10510, 40T10511

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle Type	Size	Order	Representative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $	$1$	$1$	$()$
$ 2, 2, 1, 1, 1, 1, 1, 1 $	$100$	$2$	$( 1, 3)( 6, 8)$
$ 2, 2, 2, 2, 1, 1 $	$225$	$2$	$( 1, 3)( 2,10)( 5, 7)( 6, 8)$
$ 3, 3, 1, 1, 1, 1 $	$400$	$3$	$( 1, 3, 5)( 2, 6, 8)$
$ 3, 3, 2, 2 $	$400$	$6$	$( 1, 3, 5)( 2, 6, 8)( 4,10)( 7, 9)$
$ 4, 4, 1, 1 $	$900$	$4$	$( 1, 3, 5, 7)( 2,10, 6, 8)$
$ 5, 5 $	$576$	$5$	$( 1, 3, 5, 7, 9)( 2,10, 4, 6, 8)$
$ 2, 2, 1, 1, 1, 1, 1, 1 $	$30$	$2$	$( 2,10)( 6, 8)$
$ 3, 1, 1, 1, 1, 1, 1, 1 $	$40$	$3$	$( 2, 6, 8)$
$ 5, 1, 1, 1, 1, 1 $	$48$	$5$	$( 2,10, 4, 6, 8)$
$ 3, 2, 2, 1, 1, 1 $	$400$	$6$	$( 1, 3)( 2, 6, 8)( 4,10)$
$ 4, 2, 1, 1, 1, 1 $	$600$	$4$	$( 1, 3)( 2,10, 6, 8)$
$ 3, 2, 2, 1, 1, 1 $	$600$	$6$	$( 1, 3)( 2, 6, 8)( 5, 7)$
$ 5, 2, 2, 1 $	$720$	$10$	$( 1, 3)( 2,10, 4, 6, 8)( 5, 7)$
$ 5, 3, 1, 1 $	$960$	$15$	$( 1, 3, 5)( 2,10, 4, 6, 8)$
$ 4, 3, 2, 1 $	$1200$	$12$	$( 1, 3, 5)( 2,10, 6, 8)( 7, 9)$
$ 4, 2, 2, 2 $	$600$	$4$	$( 1, 6)( 2, 5)( 3, 8)( 4, 7,10, 9)$
$ 6, 4 $	$1200$	$12$	$( 1, 8, 3, 2, 5, 6)( 4, 7,10, 9)$
$ 8, 2 $	$1800$	$8$	$( 1, 4, 7, 8, 3,10, 9, 6)( 2, 5)$
$ 4, 2, 2, 2 $	$600$	$4$	$( 1, 6)( 2, 5)( 3, 8)( 4, 9,10, 7)$
$ 6, 4 $	$1200$	$12$	$( 1, 8, 3, 2, 5, 6)( 4, 9,10, 7)$
$ 8, 2 $	$1800$	$8$	$( 1,10, 7, 8, 3, 4, 9, 6)( 2, 5)$

Group invariants

Order:		$14400=2^{6} \cdot 3^{2} \cdot 5^{2}$
Cyclic:		No
Abelian:		No
Solvable:		No
GAP id:		Data not available

Character table: Data not available.