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)
$|\Aut(F/K)|$:		$1$
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, 1, 1, 1, 1, 1, 1, 1, 1 $	$330$	$3$	$( 8, 9,11)$
$ 7, 1, 1, 1, 1 $	$237600$	$7$	$( 1, 5, 4, 6,10, 3, 7)$
$ 7, 3, 1 $	$950400$	$21$	$( 1, 3, 6, 5, 7,10, 4)( 8, 9,11)$
$ 7, 3, 1 $	$950400$	$21$	$( 1, 3, 6, 5, 7,10, 4)( 8,11, 9)$
$ 2, 2, 2, 2, 1, 1, 1 $	$17325$	$2$	$( 1, 8)( 2, 3)( 4,10)( 9,11)$
$ 4, 4, 1, 1, 1 $	$207900$	$4$	$( 1, 9, 8,11)( 2,10, 3, 4)$
$ 8, 2, 1 $	$2494800$	$8$	$( 1, 4, 9, 2, 8,10,11, 3)( 5, 7)$
$ 2, 2, 1, 1, 1, 1, 1, 1, 1 $	$990$	$2$	$( 1, 8)( 9,11)$
$ 4, 2, 1, 1, 1, 1, 1 $	$41580$	$4$	$( 1, 9, 8,11)( 5, 7)$
$ 3, 2, 2, 1, 1, 1, 1 $	$69300$	$6$	$( 1, 8)( 2, 4,10)( 9,11)$
$ 4, 3, 2, 1, 1 $	$831600$	$12$	$( 1,11, 8, 9)( 2,10, 4)( 3, 6)$
$ 5, 1, 1, 1, 1, 1, 1 $	$11088$	$5$	$( 2, 3,10, 6, 4)$
$ 5, 2, 2, 1, 1 $	$498960$	$10$	$( 1, 8)( 2, 6, 3, 4,10)( 9,11)$
$ 5, 4, 2 $	$997920$	$20$	$( 1, 9, 8,11)( 2, 4, 6,10, 3)( 5, 7)$
$ 3, 3, 1, 1, 1, 1, 1 $	$18480$	$3$	$( 1, 6,10)( 2, 3, 9)$
$ 4, 2, 2, 2, 1 $	$207900$	$4$	$( 1, 9)( 2, 6)( 3,10)( 4,11, 8, 5)$
$ 3, 3, 2, 2, 1 $	$277200$	$6$	$( 1,10, 6)( 2, 9, 3)( 4, 8)( 5,11)$
$ 6, 4, 1 $	$1663200$	$12$	$( 1, 2,10, 9, 6, 3)( 4, 5, 8,11)$
$ 11 $	$1814400$	$11$	$( 1, 7,10, 8, 3, 5, 9, 4, 6,11, 2)$
$ 11 $	$1814400$	$11$	$( 1, 2,11, 6, 4, 9, 5, 3, 8,10, 7)$
$ 3, 3, 3, 1, 1 $	$123200$	$3$	$( 1, 2,11)( 3, 7, 5)( 6, 8,10)$
$ 9, 1, 1 $	$2217600$	$9$	$( 1,10, 3, 2, 6, 7,11, 8, 5)$
$ 6, 3, 2 $	$1108800$	$6$	$( 1, 2,11)( 3,10, 7, 6, 5, 8)( 4, 9)$
$ 3, 2, 2, 2, 2 $	$34650$	$6$	$( 1, 9)( 2, 4)( 3,10)( 5, 6, 7)( 8,11)$
$ 4, 4, 3 $	$415800$	$12$	$( 1, 4, 9, 2)( 3, 8,10,11)( 5, 7, 6)$
$ 6, 2, 1, 1, 1 $	$554400$	$6$	$( 1, 5,11, 7, 6,10)( 3, 4)$
$ 5, 3, 3 $	$443520$	$15$	$( 1, 6,10)( 2, 9, 3)( 4, 8, 7, 5,11)$
$ 5, 3, 1, 1, 1 $	$443520$	$15$	$( 2, 9, 3)( 4, 7,11, 8, 5)$
$ 7, 2, 2 $	$712800$	$14$	$( 1, 8)( 2, 4, 6, 5, 7, 3,10)( 9,11)$
$ 5, 5, 1 $	$798336$	$5$	$( 1, 4, 3, 9, 5)( 6,11, 8, 7,10)$

Group invariants

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

Character table: not available.