Galois group: 12T295

• Label: 12T295
• Degree: $12$
• Order: $95040$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: yes
• $p$-group: no
• Group: $M_{12}$

Group action invariants

Degree $n$:		$12$
Transitive number $t$:		$295$
Group:		$M_{12}$
CHM label:		$M(12)$
Parity:		$1$
Primitive:		yes
$\card{\Aut(F/K)}$:		$1$
Generators:		(1,9,5,12,11,8,2,4)(6,10), (1,11,2,3,4)(5,8,12,6,7)

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

12T295

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	Representative
	$1^{12}$	$1$	$1$	$()$
	$5^{2},1^{2}$	$9504$	$5$	$( 1, 3, 8, 6, 9)( 4,10, 7,11, 5)$
	$2^{6}$	$396$	$2$	$( 1, 5)( 2,12)( 3, 4)( 6, 7)( 8,10)( 9,11)$
	$10,2$	$9504$	$10$	$( 1,11, 6,10, 3, 5, 9, 7, 8, 4)( 2,12)$
	$3^{4}$	$2640$	$3$	$( 1, 3,11)( 2, 5, 4)( 6, 8,12)( 7,10, 9)$
	$2^{4},1^{4}$	$495$	$2$	$( 3, 9)( 4,11)( 6, 8)( 7,10)$
	$4^{2},1^{4}$	$2970$	$4$	$( 3, 8, 9, 6)( 4,10,11, 7)$
	$4^{2},2^{2}$	$2970$	$4$	$( 1,11)( 2,12, 7, 8)( 3, 5)( 4, 9,10, 6)$
	$8,4$	$11880$	$8$	$( 1, 5,11, 3)( 2, 4,12, 9, 7,10, 8, 6)$
	$11,1$	$8640$	$11$	$( 1,10, 4, 3, 2, 5, 7,12, 9, 8,11)$
	$11,1$	$8640$	$11$	$( 1,11, 8, 9,12, 7, 5, 2, 3, 4,10)$
	$3^{3},1^{3}$	$1760$	$3$	$( 1, 7, 8)( 2, 9, 3)( 5,10,11)$
	$6,3,2,1$	$15840$	$6$	$( 1, 5, 7,10, 8,11)( 2, 3, 9)( 4,12)$
	$8,2,1^{2}$	$11880$	$8$	$( 1, 4,11, 3, 7, 5, 9,12)( 6, 8)$
	$6^{2}$	$7920$	$6$	$( 1, 7,12, 6, 9, 4)( 2, 8,10,11, 5, 3)$

Group invariants

Order:		$95040=2^{6} \cdot 3^{3} \cdot 5 \cdot 11$
Cyclic:		no
Abelian:		no
Solvable:		no
Nilpotency class:		not nilpotent
Label:		95040.a
Character table:

	Size
	2 P
	3 P
	5 P
	11 P
	Type