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 $ | $1155$ | $2$ | $( 1,20)( 2, 4)( 3,11)( 5,13)( 6,15)( 7,14)( 8,19)(10,18)$ |
| $ 4, 4, 4, 4, 2, 2, 1, 1 $ | $13860$ | $4$ | $( 1,14,20, 7)( 2,19, 4, 8)( 3,10,11,18)( 5, 6,13,15)(12,21)(17,22)$ |
| $ 8, 8, 4, 1, 1 $ | $55440$ | $8$ | $( 1,19,14, 4,20, 8, 7, 2)( 3,15,10, 5,11, 6,18,13)(12,22,21,17)$ |
| $ 4, 4, 4, 4, 2, 2, 2 $ | $9240$ | $4$ | $( 1, 5,20,13)( 2, 7, 4,14)( 3,15,11, 6)( 8,18,19,10)( 9,16)(12,21)(17,22)$ |
| $ 3, 3, 3, 3, 3, 3, 1, 1, 1, 1 $ | $12320$ | $3$ | $( 1,14,18)( 2,19, 5)( 4, 8,13)( 7,10,20)( 9,21,17)(12,22,16)$ |
| $ 6, 6, 3, 3, 2, 2 $ | $36960$ | $6$ | $( 1,10,14,20,18, 7)( 2,13,19, 4, 5, 8)( 3,11)( 6,15)( 9,17,21)(12,16,22)$ |
| $ 12, 6, 4 $ | $73920$ | $12$ | $( 1, 4,10, 5,14, 8,20, 2,18,13, 7,19)( 3, 6,11,15)( 9,12,17,16,21,22)$ |
| $ 11, 11 $ | $80640$ | $11$ | $( 1,12,21,22, 7,17, 6,14, 9, 4,10)( 2,20,16,11,18,19, 3, 5,13, 8,15)$ |
| $ 5, 5, 5, 5, 1, 1 $ | $88704$ | $5$ | $( 1,15,14,18,11)( 2,22,17, 4,19)( 3,10, 5,12,13)( 7, 9,16,20,21)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $1386$ | $2$ | $( 1, 4)( 2,14)( 3, 9)( 5,20)( 6, 8)( 7,13)(10,16)(11,17)(12,21)(15,19)(18,22)$ |
| $ 10, 10, 2 $ | $88704$ | $10$ | $( 1,19,14,22,11, 4,15, 2,18,17)( 3,16, 5,21,13, 9,10,20,12, 7)( 6, 8)$ |
| $ 4, 4, 4, 4, 2, 1, 1, 1, 1 $ | $13860$ | $4$ | $( 2,21, 9,11)( 3,17,14,12)( 5,20)( 7,15,22,16)(10,13,19,18)$ |
| $ 8, 8, 4, 2 $ | $55440$ | $8$ | $( 1,15, 7,13,20, 6,14, 5)( 2, 3, 8,18, 4,11,19,10)( 9,16)(12,22,21,17)$ |
| $ 7, 7, 7, 1 $ | $63360$ | $7$ | $( 1,16,15,13, 7,10,21)( 2,17, 3, 8,14,18,11)( 4, 6,22,12, 9, 5,19)$ |
| $ 7, 7, 7, 1 $ | $63360$ | $7$ | $( 1,21,10, 7,13,15,16)( 2,11,18,14, 8, 3,17)( 4,19, 5, 9,12,22, 6)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 $ | $330$ | $2$ | $( 2,19)( 3, 6)( 4,17)( 5,11)( 8,22)( 9,18)(12,14)$ |
| $ 6, 6, 3, 3, 2, 1, 1 $ | $73920$ | $6$ | $( 1, 3,10,20,11,18)( 2, 8, 6)( 4,19,15)( 7,14)( 9,22,12,16,17,21)$ |
| $ 14, 7, 1 $ | $63360$ | $14$ | $( 1,10,16,15, 7,20,13)( 2,11,18,14,22, 6,17,19, 5, 9,12, 8, 3, 4)$ |
| $ 14, 7, 1 $ | $63360$ | $14$ | $( 1,15,13,16,20,10, 7)( 2,14,17, 9, 3,11,22,19,12, 4,18, 6, 5, 8)$ |
| $ 4, 4, 4, 4, 2, 2, 1, 1 $ | $27720$ | $4$ | $( 1,22)( 2,16,20, 4)( 3,13,10,15)( 5,19)( 6, 8,17,14)( 7,11, 9,12)$ |
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. |