Group action invariants
| Degree $n$: | $22$ | |
| Transitive number $t$: | $41$ | |
| Parity: | $-1$ | |
| Primitive: | yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,15,18,2,9,20,13,21,17,3,4,16)(5,12,22,11,8,14)(6,10,19,7), (1,22,17,12,15)(2,5,8,20,21)(3,16,11,9,7)(4,10,6,13,18) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 11: None
Low degree siblings
44T405Siblings are shown 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, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ |
| $ 11, 11 $ | $80640$ | $11$ | $( 1,12,18,14,11,22,13, 9, 6, 8, 2)( 3, 7,21,10,17,19,15, 5,16, 4,20)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $1155$ | $2$ | $( 1,22)( 2,19)( 4,13)( 5, 6)( 8,15)(10,21)(12,18)(17,20)$ |
| $ 4, 4, 4, 4, 2, 2, 1, 1 $ | $13860$ | $4$ | $( 1, 4,22,13)( 2,10,19,21)( 5,12, 6,18)( 7,16)( 8,20,15,17)( 9,14)$ |
| $ 8, 8, 4, 1, 1 $ | $55440$ | $8$ | $( 1, 6, 4,18,22, 5,13,12)( 2, 8,10,20,19,15,21,17)( 7, 9,16,14)$ |
| $ 8, 8, 4, 2 $ | $55440$ | $8$ | $( 1,21,20,19,22,10,17, 2)( 3,16,11, 7)( 4, 6,15,18,13, 5, 8,12)( 9,14)$ |
| $ 4, 4, 4, 4, 2, 1, 1, 1, 1 $ | $13860$ | $4$ | $( 1,15,22, 8)( 2,12,19,18)( 3,11)( 4,17,13,20)( 5,10, 6,21)$ |
| $ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ | $12320$ | $3$ | $( 2,15,13)( 3, 9, 4)( 5,22,18)( 6,11,10)( 7,12,14)( 8,17,16)$ |
| $ 4, 4, 4, 4, 2, 2, 2 $ | $9240$ | $4$ | $( 1,19,21,20)( 2,18, 9, 7)( 3,14,13,22)( 4,12,15, 5)( 6,16)( 8,11)(10,17)$ |
| $ 6, 6, 3, 3, 2, 2 $ | $36960$ | $6$ | $( 1,21)( 2, 3,15, 9,13, 4)( 5, 7,22,12,18,14)( 6,10,11)( 8,16,17)(19,20)$ |
| $ 12, 6, 4 $ | $73920$ | $12$ | $( 1,20,21,19)( 2,12, 3,18,15,14, 9, 5,13, 7, 4,22)( 6, 8,10,16,11,17)$ |
| $ 7, 7, 7, 1 $ | $63360$ | $7$ | $( 1,19, 2,10, 4, 9, 5)( 3,22,13,16,14, 8,17)( 7,11,12,18,15,21,20)$ |
| $ 7, 7, 7, 1 $ | $63360$ | $7$ | $( 1, 5, 9, 4,10, 2,19)( 3,17, 8,14,16,13,22)( 7,20,21,15,18,12,11)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $1386$ | $2$ | $( 1, 2)( 3, 5)( 4,14)( 6,15)( 7,17)( 8,21)( 9,11)(10,13)(12,19)(16,18)(20,22)$ |
| $ 5, 5, 5, 5, 1, 1 $ | $88704$ | $5$ | $( 1, 5,12,10,16)( 2, 3,19,13,18)( 4,11, 7, 6,22)( 9,17,15,20,14)$ |
| $ 10, 10, 2 $ | $88704$ | $10$ | $( 1,13, 5,18,12, 2,10, 3,16,19)( 4,15,11,20, 7,14, 6, 9,22,17)( 8,21)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $330$ | $2$ | $( 1,14)( 2,17)( 3,10)( 4,22)( 5,16)( 8,19)( 9,13)$ |
| $ 14, 7, 1 $ | $63360$ | $14$ | $( 1, 3, 5,17, 9, 8, 4,14,10,16, 2,13,19,22)( 7,18,20,12,21,11,15)$ |
| $ 14, 7, 1 $ | $63360$ | $14$ | $( 1,17, 4,16,19, 3, 9,14, 2,22, 5, 8,10,13)( 7,12,15,20,11,18,21)$ |
| $ 6, 6, 3, 3, 2, 1, 1 $ | $73920$ | $6$ | $( 1, 5, 9,15, 3,12)( 2, 6,20)( 4, 7,16,10, 8,22)(11,13,19)(17,21)$ |
| $ 4, 4, 4, 4, 2, 2, 1, 1 $ | $27720$ | $4$ | $( 1,15, 4,20)( 2,21,18, 5)( 3,16)( 6,19,10,12)( 7,11)( 8,13,17,22)$ |
Group invariants
| Order: | $887040=2^{8} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | no | |
| GAP id: | not available |
| Character table: not available. |