Group action invariants
| Degree $n$ : | $22$ | |
| Transitive number $t$ : | $10$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,15)(2,21)(3,16)(4,22)(5,17)(6,12)(7,18)(8,13)(9,19)(10,14)(11,20), (1,15,2,20)(3,14,11,21)(4,19,10,16)(5,13,9,22)(6,18,8,17)(7,12) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 3 4: $C_2^2$ 8: $D_{4}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
22T10, 44T39 x 2, 44T40 x 2, 44T41 x 2, 44T44 x 2Siblings 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 $ | $4$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,14,16,18,20,22,13,15,17,19,21)$ |
| $ 11, 11 $ | $4$ | $11$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,16,20,13,17,21,14,18,22,15,19)$ |
| $ 11, 11 $ | $4$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,20,17,14,22,19,16,13,21,18,15)$ |
| $ 11, 11 $ | $4$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,22,16,21,15,20,14,19,13,18)$ |
| $ 11, 11 $ | $4$ | $11$ | $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22,21,20,19,18,17,16,15,14,13)$ |
| $ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $4$ | $11$ | $(12,16,20,13,17,21,14,18,22,15,19)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,18,13,19,14,20,15,21,16,22,17)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,20,17,14,22,19,16,13,21,18,15)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,13,14,15,16,17,18,19,20,21,22)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,22,21,20,19,18,17,16,15,14,13)$ |
| $ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $4$ | $11$ | $(12,20,17,14,22,19,16,13,21,18,15)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,22,21,20,19,18,17,16,15,14,13)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,13,14,15,16,17,18,19,20,21,22)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,17,22,16,21,15,20,14,19,13,18)$ |
| $ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $4$ | $11$ | $(12,17,22,16,21,15,20,14,19,13,18)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,19,15,22,18,14,21,17,13,20,16)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,14,16,18,20,22,13,15,17,19,21)$ |
| $ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $4$ | $11$ | $(12,22,21,20,19,18,17,16,15,14,13)$ |
| $ 11, 11 $ | $8$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,16,20,13,17,21,14,18,22,15,19)$ |
| $ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $4$ | $11$ | $(12,21,19,17,15,13,22,20,18,16,14)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 $ | $22$ | $2$ | $( 1,15)( 2,21)( 3,16)( 4,22)( 5,17)( 6,12)( 7,18)( 8,13)( 9,19)(10,14)(11,20)$ |
| $ 22 $ | $44$ | $22$ | $( 1,19, 9,12, 6,16, 3,20,11,13, 8,17, 5,21, 2,14,10,18, 7,22, 4,15)$ |
| $ 22 $ | $44$ | $22$ | $( 1,12, 6,20,11,17, 5,14,10,22, 4,19, 9,16, 3,13, 8,21, 2,18, 7,15)$ |
| $ 22 $ | $44$ | $22$ | $( 1,20,11,14,10,19, 9,13, 8,18, 7,12, 6,17, 5,22, 4,16, 3,21, 2,15)$ |
| $ 22 $ | $44$ | $22$ | $( 1,14,10,13, 8,12, 6,22, 4,21, 2,20,11,19, 9,18, 7,17, 5,16, 3,15)$ |
| $ 22 $ | $44$ | $22$ | $( 1,13, 8,22, 4,20,11,18, 7,16, 3,14,10,12, 6,21, 2,19, 9,17, 5,15)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ | $121$ | $2$ | $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)$ |
| $ 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 $ | $44$ | $22$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,14)(15,22)(16,21)(17,20)(18,19)$ |
| $ 11, 2, 2, 2, 2, 2, 1 $ | $44$ | $22$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,16)(13,15)(17,22)(18,21)(19,20)$ |
| $ 11, 2, 2, 2, 2, 2, 1 $ | $44$ | $22$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,20)(13,19)(14,18)(15,17)(21,22)$ |
| $ 11, 2, 2, 2, 2, 2, 1 $ | $44$ | $22$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17)(13,16)(14,15)(18,22)(19,21)$ |
| $ 11, 2, 2, 2, 2, 2, 1 $ | $44$ | $22$ | $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22)(13,21)(14,20)(15,19)(16,18)$ |
| $ 4, 4, 4, 4, 4, 2 $ | $242$ | $4$ | $( 1,15,11,20)( 2,21,10,14)( 3,16, 9,19)( 4,22, 8,13)( 5,17, 7,18)( 6,12)$ |
Group invariants
| Order: | $968=2^{3} \cdot 11^{2}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | [968, 36] |
| Character table: Data not available. |