Galois group: 10T41

• Label: 10T41
• Degree: $10$
• Order: $14400$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: no
• $p$-group: no
• Group: $(A_5^2 : C_2):C_2$

Group action invariants

Degree $n$:		$10$
Transitive number $t$:		$41$
Group:		$(A_5^2 : C_2):C_2$
CHM label:		$[1/2.S(5)^{2}]2=[A(5):2]2$
Parity:		$-1$
Primitive:		no
Nilpotency class:		$-1$ (not nilpotent)
$\card{\Aut(F/K)}$:		$1$
Generators:		(2,10)(5,7), (2,4,6,8,10), (1,6)(2,7)(3,8)(4,9)(5,10)

Low degree resolvents

|G/N|	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_2^2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 5: None

Low degree siblings

12T279, 20T456, 20T459, 24T12117, 25T101, 30T819, 36T9862, 40T10506, 40T10507, 40T10508

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 $	$400$	$3$	$( 1, 3, 5)( 6, 8,10)$
$ 3, 3, 2, 2 $	$400$	$6$	$( 1, 3, 5)( 2, 4)( 6, 8,10)( 7, 9)$
$ 4, 4, 1, 1 $	$900$	$4$	$( 1, 3, 5, 7)( 2, 6, 8,10)$
$ 5, 5 $	$288$	$5$	$( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)$
$ 5, 5 $	$288$	$5$	$( 1, 3, 5, 7, 9)( 2, 6, 8,10, 4)$
$ 2, 2, 1, 1, 1, 1, 1, 1 $	$30$	$2$	$( 2,10)( 6, 8)$
$ 3, 1, 1, 1, 1, 1, 1, 1 $	$40$	$3$	$( 6, 8,10)$
$ 5, 1, 1, 1, 1, 1 $	$48$	$5$	$( 2, 4, 6, 8,10)$
$ 3, 2, 2, 1, 1, 1 $	$400$	$6$	$( 1, 3)( 2, 4)( 6, 8,10)$
$ 4, 2, 1, 1, 1, 1 $	$600$	$4$	$( 1, 3)( 2, 6, 8,10)$
$ 3, 2, 2, 1, 1, 1 $	$600$	$6$	$( 1, 3)( 5, 7)( 6, 8,10)$
$ 5, 2, 2, 1 $	$720$	$10$	$( 1, 3)( 2, 4, 6, 8,10)( 5, 7)$
$ 5, 3, 1, 1 $	$960$	$15$	$( 1, 3, 5)( 2, 4, 6, 8,10)$
$ 4, 3, 2, 1 $	$1200$	$12$	$( 1, 3, 5)( 2, 6, 8,10)( 7, 9)$
$ 2, 2, 2, 2, 2 $	$60$	$2$	$( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)$
$ 4, 4, 2 $	$900$	$4$	$( 1, 8, 3, 6)( 2, 7,10, 5)( 4, 9)$
$ 6, 2, 2 $	$1200$	$6$	$( 1, 8, 3,10, 5, 6)( 2, 7)( 4, 9)$
$ 10 $	$1440$	$10$	$( 1, 8, 3,10, 5, 2, 7, 4, 9, 6)$
$ 2, 2, 2, 2, 2 $	$60$	$2$	$( 1, 8)( 2, 7)( 3, 6)( 4, 9)( 5,10)$
$ 6, 2, 2 $	$1200$	$6$	$( 1, 8)( 2, 7, 4, 9,10, 5)( 3, 6)$
$ 4, 4, 2 $	$900$	$4$	$( 1, 6, 3, 8)( 2, 7,10, 5)( 4, 9)$
$ 10 $	$1440$	$10$	$( 1,10, 5, 2, 7, 6, 3, 4, 9, 8)$

Group invariants

Order:		$14400=2^{6} \cdot 3^{2} \cdot 5^{2}$
Cyclic:		no
Abelian:		no
Solvable:		no
Label:		14400.c

Character table: not available.