Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $41$ | |
| Parity: | $-1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| 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) | |
| $|\Aut(F/K)|$: | $1$ |
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 $ | $1$ | $1$ | $()$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1 $ | $1155$ | $2$ | $( 2,20)( 3,16)( 4, 9)( 5,11)( 6,21)( 7,10)(14,22)(15,19)$ |
| $ 4, 4, 4, 4, 2, 2, 1, 1 $ | $13860$ | $4$ | $( 1,13)( 2, 6,20,21)( 3,15,16,19)( 4,22, 9,14)( 5,10,11, 7)(17,18)$ |
| $ 8, 8, 4, 1, 1 $ | $55440$ | $8$ | $( 1,17,13,18)( 2,11, 6, 7,20, 5,21,10)( 3,22,15, 9,16,14,19, 4)$ |
| $ 8, 8, 4, 2 $ | $55440$ | $8$ | $( 1,17,13,18)( 2, 4,21,14,20, 9, 6,22)( 3,10,19, 5,16, 7,15,11)( 8,12)$ |
| $ 5, 5, 5, 5, 1, 1 $ | $88704$ | $5$ | $( 1,21,19,18, 5)( 2,15, 9, 8,12)( 3,11, 6,14,10)( 4,20, 7,16,17)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $1386$ | $2$ | $( 1, 4)( 2,11)( 3,12)( 5,17)( 6,15)( 7,19)( 8,10)( 9,14)(13,22)(16,18)(20,21)$ |
| $ 10, 10, 2 $ | $88704$ | $10$ | $( 1, 7, 5,20,18, 4,19,17,21,16)( 2,14,12, 6, 8,11, 9, 3,15,10)(13,22)$ |
| $ 11, 11 $ | $80640$ | $11$ | $( 1,13,19, 8, 3, 4,20, 5,14,15, 9)( 2,16,10,11,21, 6,18, 7,17,12,22)$ |
| $ 4, 4, 4, 4, 2, 1, 1, 1, 1 $ | $13860$ | $4$ | $( 1, 5,10, 7)( 3,14,15,21)( 4,17, 8,19)( 6,20,12, 9)(16,18)$ |
| $ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ | $12320$ | $3$ | $( 1,18, 8)( 2,16, 6)( 3,21,20)( 5, 7,14)(10,22,11)(12,13,17)$ |
| $ 6, 6, 3, 3, 2, 2 $ | $36960$ | $6$ | $( 1, 8,18)( 2,21,16,20, 6, 3)( 4, 9)( 5,22, 7,11,14,10)(12,17,13)(15,19)$ |
| $ 4, 4, 4, 4, 2, 2, 2 $ | $9240$ | $4$ | $( 1,13)( 2,22,20,14)( 3, 5,16,11)( 4,15, 9,19)( 6,10,21, 7)( 8,12)(17,18)$ |
| $ 12, 6, 4 $ | $73920$ | $12$ | $( 1,17, 8,13,18,12)( 2, 5,21,22,16, 7,20,11, 6,14, 3,10)( 4,19, 9,15)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $330$ | $2$ | $( 1,13)( 2,20)( 3,16)( 6,21)( 8,12)(15,19)(17,18)$ |
| $ 6, 6, 3, 3, 2, 1, 1 $ | $73920$ | $6$ | $( 1,12,18,13, 8,17)( 2, 6,16)( 3,20,21)( 4, 9)( 5,22, 7,11,14,10)$ |
| $ 7, 7, 7, 1 $ | $63360$ | $7$ | $( 1,16,18, 8, 2, 6,19)( 3,17,12,20,21,15,13)( 4,10,14, 5, 7,11, 9)$ |
| $ 7, 7, 7, 1 $ | $63360$ | $7$ | $( 1,19, 6, 2, 8,18,16)( 3,13,15,21,20,12,17)( 4, 9,11, 7, 5,14,10)$ |
| $ 14, 7, 1 $ | $63360$ | $14$ | $( 1,20,16,21,18,15, 8,13, 2, 3, 6,17,19,12)( 4, 7,10,11,14, 9, 5)$ |
| $ 14, 7, 1 $ | $63360$ | $14$ | $( 1,21, 8, 3,19,20,18,13, 6,12,16,15, 2,17)( 4,11, 5,10, 9, 7,14)$ |
| $ 4, 4, 4, 4, 2, 2, 1, 1 $ | $27720$ | $4$ | $( 1,10,14,18)( 3,22,11, 9)( 4,12)( 6,20,19, 7)( 8,17,15,16)(13,21)$ |
Group invariants
| Order: | $887040=2^{8} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |