Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $19$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,2,6,11,9)(3,10,5,7,4)(13,15,21,17,16)(14,18,19,22,20), (1,14,5,20)(2,21,4,13)(3,17)(6,16,11,18)(7,12,10,22)(8,19,9,15), (1,5)(2,4)(6,11)(7,10)(8,9)(12,15,18,21,13,16,19,22,14,17,20) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ 10: $D_{5}$ 20: $D_{10}$ 40: 20T7 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
44T81, 44T82, 44T83Siblings 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 $ | $20$ | $11$ | $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21)$ |
| $ 11, 11 $ | $20$ | $11$ | $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19)$ |
| $ 11, 11 $ | $20$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,20,17,14,22,19,16,13,21,18,15)$ |
| $ 11, 11 $ | $20$ | $11$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,17,22,16,21,15,20,14,19,13,18)$ |
| $ 11, 11 $ | $20$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,22,21,20,19,18,17,16,15,14,13)$ |
| $ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $20$ | $11$ | $(12,16,20,13,17,21,14,18,22,15,19)$ |
| $ 5, 5, 5, 5, 1, 1 $ | $242$ | $5$ | $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,15,21,17,16)(14,18,19,22,20)$ |
| $ 5, 5, 5, 5, 1, 1 $ | $242$ | $5$ | $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,21,16,15,17)(14,19,20,18,22)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $121$ | $2$ | $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)$ |
| $ 10, 10, 1, 1 $ | $242$ | $10$ | $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(13,20,21,18,16,22,15,14,17,19)$ |
| $ 10, 10, 1, 1 $ | $242$ | $10$ | $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(13,14,16,20,17,22,21,19,15,18)$ |
| $ 4, 4, 4, 4, 4, 2 $ | $1210$ | $4$ | $( 1,14, 5,20)( 2,21, 4,13)( 3,17)( 6,16,11,18)( 7,12,10,22)( 8,19, 9,15)$ |
| $ 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $22$ | $2$ | $(13,22)(14,21)(15,20)(16,19)(17,18)$ |
| $ 11, 2, 2, 2, 2, 2, 1 $ | $220$ | $22$ | $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14)(15,22)(16,21)(17,20)(18,19)$ |
| $ 10, 5, 5, 1, 1 $ | $242$ | $10$ | $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,20,21,18,16,22,15,14,17,19)$ |
| $ 10, 5, 5, 1, 1 $ | $242$ | $10$ | $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,14,16,20,17,22,21,19,15,18)$ |
| $ 10, 5, 5, 1, 1 $ | $242$ | $10$ | $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(13,19,17,14,15,22,16,18,21,20)$ |
| $ 10, 5, 5, 1, 1 $ | $242$ | $10$ | $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(13,18,15,19,21,22,17,20,16,14)$ |
| $ 22 $ | $220$ | $22$ | $( 1,14, 4,13, 7,12,10,22, 2,21, 5,20, 8,19,11,18, 3,17, 6,16, 9,15)$ |
| $ 22 $ | $220$ | $22$ | $( 1,16, 8,21, 4,15,11,20, 7,14, 3,19,10,13, 6,18, 2,12, 9,17, 5,22)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $110$ | $2$ | $( 1,18)( 2,14)( 3,21)( 4,17)( 5,13)( 6,20)( 7,16)( 8,12)( 9,19)(10,15)(11,22)$ |
| $ 22 $ | $220$ | $22$ | $( 1,19, 3,22, 5,14, 7,17, 9,20,11,12, 2,15, 4,18, 6,21, 8,13,10,16)$ |
| $ 22 $ | $220$ | $22$ | $( 1,13, 2,20, 3,16, 4,12, 5,19, 6,15, 7,22, 8,18, 9,14,10,21,11,17)$ |
| $ 22 $ | $220$ | $22$ | $( 1,21, 7,19, 2,17, 8,15, 3,13, 9,22, 4,20,10,18, 5,16,11,14, 6,12)$ |
Group invariants
| Order: | $4840=2^{3} \cdot 5 \cdot 11^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |