Group action invariants
| Degree $n$: | $33$ | |
| Transitive number $t$: | $12$ | |
| Parity: | $-1$ | |
| Primitive: | no | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| $|\Aut(F/K)|$: | $1$ | |
| Generators: | (1,19,25)(2,12,30)(3,16,24)(4,20,29)(5,13,23)(6,17,28)(7,21,33)(8,14,27)(9,18,32)(10,22,26)(11,15,31), (1,25,18,5,27,12)(2,31,22,4,32,19)(3,26,15)(6,33,16,11,30,14)(7,28,20,10,24,21)(8,23,13,9,29,17) |
Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $C_6$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: None
Low degree siblings
33T12 x 3Siblings 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, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $1$ | $1$ | $()$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,21,19,17,15,13,22,20,18,16,14) (23,32,30,28,26,24,33,31,29,27,25)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,19,15,22,18,14,21,17,13,20,16) (23,30,26,33,29,25,32,28,24,31,27)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,15,18,21,13,16,19,22,14,17,20) (23,26,29,32,24,27,30,33,25,28,31)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,18,13,19,14,20,15,21,16,22,17) (23,29,24,30,25,31,26,32,27,33,28)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,13,14,15,16,17,18,19,20,21,22) (23,24,25,26,27,28,29,30,31,32,33)$ |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $(12,13,14,15,16,17,18,19,20,21,22)(23,30,26,33,29,25,32,28,24,31,27)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22,21,20,19,18,17,16,15,14,13) (23,28,33,27,32,26,31,25,30,24,29)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,19,15,22,18,14,21,17,13,20,16) (23,25,27,29,31,33,24,26,28,30,32)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21) (23,31,28,25,33,30,27,24,32,29,26)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,15,18,21,13,16,19,22,14,17,20) (23,32,30,28,26,24,33,31,29,27,25)$ |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,17,22,16,21,15,20,14,19,13,18)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,21,19,17,15,13,22,20,18,16,14) (23,27,31,24,28,32,25,29,33,26,30)$ |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(23,29,24,30,25,31,26,32,27,33,28)$ |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $(12,14,16,18,20,22,13,15,17,19,21)(23,26,29,32,24,27,30,33,25,28,31)$ |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(23,24,25,26,27,28,29,30,31,32,33)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,21,19,17,15,13,22,20,18,16,14) (23,33,32,31,30,29,28,27,26,25,24)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19) (23,28,33,27,32,26,31,25,30,24,29)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,18,13,19,14,20,15,21,16,22,17) (23,30,26,33,29,25,32,28,24,31,27)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,19,15,22,18,14,21,17,13,20,16) (23,32,30,28,26,24,33,31,29,27,25)$ |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,15,18,21,13,16,19,22,14,17,20) (23,30,26,33,29,25,32,28,24,31,27)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $121$ | $3$ | $( 1,19,25)( 2,12,30)( 3,16,24)( 4,20,29)( 5,13,23)( 6,17,28)( 7,21,33) ( 8,14,27)( 9,18,32)(10,22,26)(11,15,31)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $121$ | $3$ | $( 1,25,19)( 2,30,12)( 3,24,16)( 4,29,20)( 5,23,13)( 6,28,17)( 7,33,21) ( 8,27,14)( 9,32,18)(10,26,22)(11,31,15)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ | $121$ | $2$ | $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,29) (24,28)(25,27)(30,33)(31,32)$ |
| $ 6, 6, 6, 6, 6, 3 $ | $121$ | $6$ | $( 1,19,24, 6,21,27)( 2,15,29, 5,14,33)( 3,22,23, 4,18,28)( 7,17,32,11,12,30) ( 8,13,26,10,16,25)( 9,20,31)$ |
| $ 6, 6, 6, 6, 6, 3 $ | $121$ | $6$ | $( 1,25,14, 7,28,16)( 2,31,18, 6,33,12)( 3,26,22, 5,27,19)( 4,32,15) ( 8,23,20,11,30,21)( 9,29,13,10,24,17)$ |
Group invariants
| Order: | $726=2 \cdot 3 \cdot 11^{2}$ | |
| Cyclic: | no | |
| Abelian: | no | |
| Solvable: | yes | |
| GAP id: | [726, 6] |
| Character table: not available. |