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