# Properties

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

# Related objects

## 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.