Galois Group: 11T7

• Label: 11T7
• Order: \(19958400\)
• n: \(11\)
• 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)
Generators:		(1,2,3), (3,4,5,6,7,8,9,10,11)
$|\Aut(F/K)|$:		$1$

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

Group invariants

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

Character table: Data not available.