Properties

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

Related objects

Learn more about

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 TypeSizeOrderRepresentative
$ 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.