Galois group: 11T7

• Label: 11T7
• Degree: $11$
• Order: $19958400$
• Cyclic: no
• Abelian: no
• Solvable: no
• Primitive: yes
• $p$-group: no
• Group: $A_{11}$

Group action invariants

Degree $n$:		$11$
Transitive number $t$:		$7$
Group:		$A_{11}$
CHM label:		$A11$
Parity:		$1$
Primitive:		yes
Nilpotency class:		$-1$ (not nilpotent)
$\card{\Aut(F/K)}$:		$1$
Generators:		(1,2,3), (3,4,5,6,7,8,9,10,11)

Low degree resolvents

none

Resolvents shown for degrees $\leq 47$

Subfields

Prime degree - none

Low degree siblings

There are no siblings 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 $	$1$	$1$	$()$
$ 3, 3, 3, 1, 1 $	$123200$	$3$	$( 1,11, 7)( 2, 6, 4)( 5,10, 9)$
$ 9, 1, 1 $	$2217600$	$9$	$( 1, 2, 5,11, 6,10, 7, 4, 9)$
$ 2, 2, 2, 2, 1, 1, 1 $	$17325$	$2$	$( 1, 7)( 2, 5)( 8,11)( 9,10)$
$ 4, 4, 1, 1, 1 $	$207900$	$4$	$( 1, 5, 7, 2)( 8, 9,11,10)$
$ 3, 1, 1, 1, 1, 1, 1, 1, 1 $	$330$	$3$	$(3,4,6)$
$ 3, 2, 2, 2, 2 $	$34650$	$6$	$( 1, 7)( 2, 5)( 3, 6, 4)( 8,11)( 9,10)$
$ 4, 4, 3 $	$415800$	$12$	$( 1,10, 7, 9)( 2,11, 5, 8)( 3, 4, 6)$
$ 7, 1, 1, 1, 1 $	$237600$	$7$	$( 1, 7, 9, 5,11, 2, 8)$
$ 7, 3, 1 $	$950400$	$21$	$( 1, 7, 9, 5,11, 2, 8)( 4, 6,10)$
$ 7, 3, 1 $	$950400$	$21$	$( 1, 7, 9, 5,11, 2, 8)( 4,10, 6)$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1 $	$990$	$2$	$( 1, 4)( 7,10)$
$ 5, 1, 1, 1, 1, 1, 1 $	$11088$	$5$	$( 2,11, 5, 8, 3)$
$ 5, 2, 2, 1, 1 $	$498960$	$10$	$( 1, 4)( 2, 8,11, 3, 5)( 7,10)$
$ 4, 2, 1, 1, 1, 1, 1 $	$41580$	$4$	$( 1, 7, 4,10)( 6, 9)$
$ 5, 4, 2 $	$997920$	$20$	$( 1, 7, 4,10)( 2,11, 5, 8, 3)( 6, 9)$
$ 11 $	$1814400$	$11$	$( 1, 6, 4, 5,10, 3, 8,11, 9, 7, 2)$
$ 11 $	$1814400$	$11$	$( 1, 2, 7, 9,11, 8, 3,10, 5, 4, 6)$
$ 3, 2, 2, 1, 1, 1, 1 $	$69300$	$6$	$( 1,10, 5)( 2, 3)( 7, 8)$
$ 4, 3, 2, 1, 1 $	$831600$	$12$	$( 1, 5,10)( 2, 7, 3, 8)( 4,11)$
$ 3, 3, 1, 1, 1, 1, 1 $	$18480$	$3$	$( 1, 5, 9)( 2,10, 7)$
$ 3, 3, 2, 2, 1 $	$277200$	$6$	$( 1, 9, 5)( 2, 7,10)( 3, 4)( 8,11)$
$ 4, 2, 2, 2, 1 $	$207900$	$4$	$( 1,10)( 2, 9)( 3,11, 4, 8)( 5, 7)$
$ 6, 4, 1 $	$1663200$	$12$	$( 1, 7, 9,10, 5, 2)( 3, 8, 4,11)$
$ 8, 2, 1 $	$2494800$	$8$	$( 1, 6, 9,11, 2, 8, 5, 4)( 7,10)$
$ 7, 2, 2 $	$712800$	$14$	$( 1,11, 6, 4, 3,10, 8)( 2, 7)( 5, 9)$
$ 6, 3, 2 $	$1108800$	$6$	$( 1, 9, 4)( 2, 8)( 3, 7, 5,11, 6,10)$
$ 6, 2, 1, 1, 1 $	$554400$	$6$	$( 1, 4)( 2, 8, 9, 3,11, 6)$
$ 5, 3, 3 $	$443520$	$15$	$( 1, 5,10,11, 6)( 2, 8, 3)( 4, 9, 7)$
$ 5, 3, 1, 1, 1 $	$443520$	$15$	$( 1, 2, 9, 7, 3)( 5,11,10)$
$ 5, 5, 1 $	$798336$	$5$	$( 1,11, 3, 7, 9)( 2, 6, 8,10, 5)$

Group invariants

Order:		$19958400=2^{7} \cdot 3^{4} \cdot 5^{2} \cdot 7 \cdot 11$
Cyclic:		no
Abelian:		no
Solvable:		no
Label:		not available

Character table: not available.