Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $35$ | |
| Parity: | $1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,23,30,25,4,2,24,28,26,5,3,22,29,27,6)(7,16,21,33,11,8,17,19,31,12,9,18,20,32,10)(13,15,14), (4,28,20,14)(5,29,21,15)(6,30,19,13)(7,17,23,27)(8,18,24,25)(9,16,22,26) | |
| $|\Aut(F/K)|$: | $3$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 3: $C_3$ 7920: $M_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: $M_{11}$
Low degree siblings
36T12768Siblings 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 $ | $1$ | $1$ | $()$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $1$ | $3$ | $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)(28,29,30)(31,32,33)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $1$ | $3$ | $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20) (22,24,23)(25,27,26)(28,30,29)(31,33,32)$ |
| $ 11, 11, 11 $ | $720$ | $11$ | $( 1,31,24,18,25,21,29,10, 8, 5,15)( 2,32,22,16,26,19,30,11, 9, 6,13) ( 3,33,23,17,27,20,28,12, 7, 4,14)$ |
| $ 33 $ | $720$ | $33$ | $( 1,32,23,18,26,20,29,11, 7, 5,13, 3,31,22,17,25,19,28,10, 9, 4,15, 2,33,24, 16,27,21,30,12, 8, 6,14)$ |
| $ 33 $ | $720$ | $33$ | $( 1,33,22,18,27,19,29,12, 9, 5,14, 2,31,23,16,25,20,30,10, 7, 6,15, 3,32,24, 17,26,21,28,11, 8, 4,13)$ |
| $ 33 $ | $720$ | $33$ | $( 1,14, 6, 8,12,30,21,27,16,24,33, 2,15, 4, 9,10,28,19,25,17,22,31, 3,13, 5, 7,11,29,20,26,18,23,32)$ |
| $ 11, 11, 11 $ | $720$ | $11$ | $( 1,15, 5, 8,10,29,21,25,18,24,31)( 2,13, 6, 9,11,30,19,26,16,22,32) ( 3,14, 4, 7,12,28,20,27,17,23,33)$ |
| $ 33 $ | $720$ | $33$ | $( 1,13, 4, 8,11,28,21,26,17,24,32, 3,15, 6, 7,10,30,20,25,16,23,31, 2,14, 5, 9,12,29,19,27,18,22,33)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $440$ | $3$ | $( 1, 3, 2)( 4,26,10)( 5,27,11)( 6,25,12)( 7,19,31)( 8,20,32)( 9,21,33) (13,15,14)(16,29,23)(17,30,24)(18,28,22)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1 $ | $440$ | $3$ | $( 4,27,12)( 5,25,10)( 6,26,11)( 7,20,33)( 8,21,31)( 9,19,32)(16,30,22) (17,28,23)(18,29,24)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $440$ | $3$ | $( 1, 2, 3)( 4,25,11)( 5,26,12)( 6,27,10)( 7,21,32)( 8,19,33)( 9,20,31) (13,14,15)(16,28,24)(17,29,22)(18,30,23)$ |
| $ 6, 6, 6, 6, 3, 3, 3 $ | $165$ | $6$ | $( 1, 4, 2, 5, 3, 6)( 7,30, 8,28, 9,29)(10,12,11)(13,31,14,32,15,33)(16,18,17) (19,25,20,26,21,27)(22,24,23)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $165$ | $2$ | $( 1, 5)( 2, 6)( 3, 4)( 7,28)( 8,29)( 9,30)(13,32)(14,33)(15,31)(19,26)(20,27) (21,25)$ |
| $ 6, 6, 6, 6, 3, 3, 3 $ | $165$ | $6$ | $( 1, 6, 3, 5, 2, 4)( 7,29, 9,28, 8,30)(10,11,12)(13,33,15,32,14,31)(16,17,18) (19,27,21,26,20,25)(22,23,24)$ |
| $ 12, 12, 3, 3, 3 $ | $990$ | $12$ | $( 1, 7, 6,29, 3, 9, 5,28, 2, 8, 4,30)(10,12,11)(13,25,33,19,15,27,32,21,14,26, 31,20)(16,18,17)(22,24,23)$ |
| $ 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $990$ | $4$ | $( 1, 8, 5,29)( 2, 9, 6,30)( 3, 7, 4,28)(13,26,32,19)(14,27,33,20)(15,25,31,21)$ |
| $ 12, 12, 3, 3, 3 $ | $990$ | $12$ | $( 1, 9, 4,29, 2, 7, 5,30, 3, 8, 6,28)(10,11,12)(13,27,31,19,14,25,32,20,15,26, 33,21)(16,17,18)(22,23,24)$ |
| $ 24, 6, 3 $ | $990$ | $24$ | $( 1,13, 7,25, 6,33,29,19, 3,15, 9,27, 5,32,28,21, 2,14, 8,26, 4,31,30,20) (10,11,12)(16,23,18,22,17,24)$ |
| $ 24, 6, 3 $ | $990$ | $24$ | $( 1,14, 9,25, 4,32,29,20, 2,15, 7,26, 5,33,30,21, 3,13, 8,27, 6,31,28,19) (10,12,11)(16,24,17,22,18,23)$ |
| $ 8, 8, 8, 2, 2, 2, 1, 1, 1 $ | $990$ | $8$ | $( 1,15, 8,25, 5,31,29,21)( 2,13, 9,26, 6,32,30,19)( 3,14, 7,27, 4,33,28,20) (16,22)(17,23)(18,24)$ |
| $ 24, 6, 3 $ | $990$ | $24$ | $( 1,20,30,31, 4,26, 8,14, 2,21,28,32, 5,27, 9,15, 3,19,29,33, 6,25, 7,13) (10,12,11)(16,24,17,22,18,23)$ |
| $ 8, 8, 8, 2, 2, 2, 1, 1, 1 $ | $990$ | $8$ | $( 1,21,29,31, 5,25, 8,15)( 2,19,30,32, 6,26, 9,13)( 3,20,28,33, 4,27, 7,14) (16,22)(17,23)(18,24)$ |
| $ 24, 6, 3 $ | $990$ | $24$ | $( 1,19,28,31, 6,27, 8,13, 3,21,30,33, 5,26, 7,15, 2,20,29,32, 4,25, 9,14) (10,11,12)(16,23,18,22,17,24)$ |
| $ 6, 6, 6, 3, 3, 3, 2, 2, 2 $ | $1320$ | $6$ | $( 1,29,15, 5,10,18)( 2,30,13, 6,11,16)( 3,28,14, 4,12,17)( 7,27,33)( 8,25,31) ( 9,26,32)(19,22)(20,23)(21,24)$ |
| $ 6, 6, 6, 6, 3, 3, 3 $ | $1320$ | $6$ | $( 1,30,14, 5,11,17)( 2,28,15, 6,12,18)( 3,29,13, 4,10,16)( 7,25,32)( 8,26,33) ( 9,27,31)(19,23,21,22,20,24)$ |
| $ 6, 6, 6, 6, 3, 3, 3 $ | $1320$ | $6$ | $( 1,28,13, 5,12,16)( 2,29,14, 6,10,17)( 3,30,15, 4,11,18)( 7,26,31)( 8,27,32) ( 9,25,33)(19,24,20,22,21,23)$ |
| $ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ | $1584$ | $5$ | $( 1,15, 8,18,29)( 2,13, 9,16,30)( 3,14, 7,17,28)( 4,33,23,27,12) ( 5,31,24,25,10)( 6,32,22,26,11)$ |
| $ 15, 15, 3 $ | $1584$ | $15$ | $( 1,13, 7,18,30, 3,15, 9,17,29, 2,14, 8,16,28)( 4,31,22,27,10, 6,33,24,26,12, 5,32,23,25,11)(19,20,21)$ |
| $ 15, 15, 3 $ | $1584$ | $15$ | $( 1,14, 9,18,28, 2,15, 7,16,29, 3,13, 8,17,30)( 4,32,24,27,11, 5,33,22,25,12, 6,31,23,26,10)(19,21,20)$ |
Group invariants
| Order: | $23760=2^{4} \cdot 3^{3} \cdot 5 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |