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
noneResolvents 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. |