Galois group: 12T272

• Label: 12T272
• Degree: $12$
• Order: $7920$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: yes
• $p$-group: no
• Group: $M_{11}$

Group invariants

Abstract group:		$M_{11}$
Order:		$7920=2^{4} \cdot 3^{2} \cdot 5 \cdot 11$
Cyclic:		no
Abelian:		no
Solvable:		no
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$12$
Transitive number $t$:		$272$
CHM label:		$M_{11}(12)$
Parity:		$1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$1$
Generators:		$(1,7,3,10,5,9,6,12)(2,11,8,4)$, $(1,6,3,9)(2,7,12,10,4,5,11,8)$

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 3: None

Degree 4: None

Degree 6: None

Low degree siblings

11T6, 22T22

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{12}$	$1$	$1$	$0$	$()$
2A	$2^{4},1^{4}$	$165$	$2$	$4$	$( 1, 5)( 2, 3)( 4,10)( 7,11)$
3A	$3^{3},1^{3}$	$440$	$3$	$6$	$( 1,11, 9)( 2, 7,12)( 4, 6, 8)$
4A	$4^{2},2^{2}$	$990$	$4$	$8$	$( 1,12)( 2,10, 8, 3)( 4, 9)( 5, 7,11, 6)$
5A	$5^{2},1^{2}$	$1584$	$5$	$8$	$( 1,10, 9,12, 2)( 3, 7, 5, 4, 8)$
6A	$6,3,2,1$	$1320$	$6$	$8$	$( 1, 7,11,12, 9, 2)( 4, 8, 6)( 5,10)$
8A1	$8,4$	$990$	$8$	$10$	$( 1, 4,12, 9)( 2,11,10, 6, 8, 5, 3, 7)$
8A-1	$8,4$	$990$	$8$	$10$	$( 1, 4,12, 9)( 2, 5,10, 7, 8,11, 3, 6)$
11A1	$11,1$	$720$	$11$	$10$	$( 1, 5, 3, 7, 9,10, 2,11,12, 6, 4)$
11A-1	$11,1$	$720$	$11$	$10$	$( 1, 2, 5,11, 3,12, 7, 6, 9, 4,10)$

Malle's constant $a(G)$:     $1/4$

Character table

		1A	2A	3A	4A	5A	6A	8A1	8A-1	11A1	11A-1
	Size	1	165	440	990	1584	1320	990	990	720	720
	2 P	1A	1A	3A	2A	5A	3A	4A	4A	11A-1	11A1
	3 P	1A	2A	1A	4A	5A	2A	8A1	8A-1	11A1	11A-1
	5 P	1A	2A	3A	4A	1A	6A	8A-1	8A1	11A1	11A-1
	11 P	1A	2A	3A	4A	5A	6A	8A1	8A-1	1A	1A
	Type