Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $45$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (2,3)(4,11,17,25)(5,10,18,27)(6,12,16,26)(7,9)(13,22,31,30)(14,24,32,29)(15,23,33,28)(20,21), (1,12,23,4,30,21)(2,10,24,5,28,19)(3,11,22,6,29,20)(7,32,26)(8,33,27)(9,31,25)(13,17,15,16,14,18) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ 6: $S_3$ 7920: $M_{11}$ 15840: 22T26 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: $M_{11}$
Low degree siblings
36T16207Siblings 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 $ | $2$ | $3$ | $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)(28,29,30)(31,32,33)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $3$ | $2$ | $( 2, 3)( 5, 6)( 7, 9)(10,12)(13,15)(16,18)(20,21)(22,23)(26,27)(28,30)(31,33)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ | $495$ | $2$ | $( 1,31)( 2,33)( 3,32)( 4, 6)( 7,24)( 8,23)( 9,22)(10,11)(13,17)(14,16)(15,18) (19,21)(25,28)(26,30)(27,29)$ |
| $ 6, 6, 6, 6, 3, 3, 3 $ | $330$ | $6$ | $( 1,33, 3,32, 2,31)( 4, 5, 6)( 7,24, 9,23, 8,22)(10,11,12)(13,17,15,16,14,18) (19,20,21)(25,30,27,29,26,28)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $165$ | $2$ | $( 1,32)( 2,33)( 3,31)( 7,23)( 8,24)( 9,22)(13,16)(14,17)(15,18)(25,29)(26,30) (27,28)$ |
| $ 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $990$ | $4$ | $( 4,32,17,19)( 5,33,18,20)( 6,31,16,21)( 7,10,13,23)( 8,11,14,24)( 9,12,15,22)$ |
| $ 12, 12, 3, 3, 3 $ | $1980$ | $12$ | $( 1, 2, 3)( 4,33,16,19, 5,31,17,20, 6,32,18,21)( 7,11,15,23, 8,12,13,24, 9,10, 14,22)(25,26,27)(28,29,30)$ |
| $ 4, 4, 4, 4, 4, 4, 2, 2, 2, 1, 1, 1 $ | $2970$ | $4$ | $( 2, 3)( 4,32,17,19)( 5,31,18,21)( 6,33,16,20)( 7,12,13,22)( 8,11,14,24) ( 9,10,15,23)(26,27)(28,30)$ |
| $ 24, 6, 3 $ | $1980$ | $24$ | $( 1,30, 3,29, 2,28)( 4, 9,31,11,18,13,19,22, 6, 8,33,10,17,15,21,24, 5, 7,32, 12,16,14,20,23)(25,26,27)$ |
| $ 8, 8, 8, 2, 2, 2, 1, 1, 1 $ | $990$ | $8$ | $( 1,29)( 2,30)( 3,28)( 4, 8,32,11,17,14,19,24)( 5, 9,33,12,18,15,20,22) ( 6, 7,31,10,16,13,21,23)$ |
| $ 8, 8, 8, 2, 2, 2, 2, 1 $ | $2970$ | $8$ | $( 1,28)( 2,30)( 3,29)( 4, 7,32,10,17,13,19,23)( 5, 9,33,12,18,15,20,22) ( 6, 8,31,11,16,14,21,24)(25,27)$ |
| $ 8, 8, 8, 2, 2, 2, 2, 1 $ | $2970$ | $8$ | $( 1,30)( 2,29)( 3,28)( 4,22,19,15,17,12,32, 9)( 5,24,20,14,18,11,33, 8) ( 6,23,21,13,16,10,31, 7)(25,26)$ |
| $ 24, 6, 3 $ | $1980$ | $24$ | $( 1,28, 2,29, 3,30)( 4,23,20,14,16,12,32, 7, 5,24,21,15,17,10,33, 8, 6,22,19, 13,18,11,31, 9)(25,27,26)$ |
| $ 8, 8, 8, 2, 2, 2, 1, 1, 1 $ | $990$ | $8$ | $( 1,29)( 2,30)( 3,28)( 4,24,19,14,17,11,32, 8)( 5,22,20,15,18,12,33, 9) ( 6,23,21,13,16,10,31, 7)$ |
| $ 6, 6, 6, 3, 3, 3, 2, 2, 1, 1 $ | $1320$ | $6$ | $( 2, 3)( 4,32,24)( 5,31,22, 6,33,23)( 7,26,13, 9,27,15)( 8,25,14) (10,20,16,12,21,18)(11,19,17)(28,30)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1 $ | $440$ | $3$ | $( 4,32,24)( 5,33,22)( 6,31,23)( 7,27,13)( 8,25,14)( 9,26,15)(10,21,16) (11,19,17)(12,20,18)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $880$ | $3$ | $( 1, 2, 3)( 4,33,23)( 5,31,24)( 6,32,22)( 7,25,15)( 8,26,13)( 9,27,14) (10,19,18)(11,20,16)(12,21,17)(28,29,30)$ |
| $ 6, 6, 6, 6, 3, 3, 3 $ | $2640$ | $6$ | $( 1,31, 2,32, 3,33)( 4,10, 9,29,27,15)( 5,11, 7,30,25,13)( 6,12, 8,28,26,14) (16,20,24)(17,21,22)(18,19,23)$ |
| $ 6, 6, 6, 3, 3, 3, 2, 2, 2 $ | $1320$ | $6$ | $( 1,32)( 2,33)( 3,31)( 4,11, 8,29,25,14)( 5,12, 9,30,26,15)( 6,10, 7,28,27,13) (16,21,23)(17,19,24)(18,20,22)$ |
| $ 6, 6, 6, 6, 3, 2, 2, 2 $ | $3960$ | $6$ | $( 1,33)( 2,32)( 3,31)( 4,12, 8,30,25,15)( 5,11, 9,29,26,14)( 6,10, 7,28,27,13) (16,21,23)(17,20,24,18,19,22)$ |
| $ 33 $ | $1440$ | $33$ | $( 1,22,16,19, 5,31,29,26, 7,14,12, 3,24,18,21, 4,33,28,25, 9,13,11, 2,23,17, 20, 6,32,30,27, 8,15,10)$ |
| $ 11, 11, 11 $ | $720$ | $11$ | $( 1,24,17,19, 4,32,29,25, 8,14,11)( 2,22,18,20, 5,33,30,26, 9,15,12) ( 3,23,16,21, 6,31,28,27, 7,13,10)$ |
| $ 22, 11 $ | $2160$ | $22$ | $( 1,23,17,21, 4,31,29,27, 8,13,11, 3,24,16,19, 6,32,28,25, 7,14,10) ( 2,22,18,20, 5,33,30,26, 9,15,12)$ |
| $ 22, 11 $ | $2160$ | $22$ | $( 1,11,14, 8,25,29,32, 4,19,17,24)( 2,10,15, 7,26,28,33, 6,20,16,22, 3,12,13, 9,27,30,31, 5,21,18,23)$ |
| $ 11, 11, 11 $ | $720$ | $11$ | $( 1,11,14, 8,25,29,32, 4,19,17,24)( 2,12,15, 9,26,30,33, 5,20,18,22) ( 3,10,13, 7,27,28,31, 6,21,16,23)$ |
| $ 33 $ | $1440$ | $33$ | $( 1,12,13, 8,26,28,32, 5,21,17,22, 3,11,15, 7,25,30,31, 4,20,16,24, 2,10,14, 9,27,29,33, 6,19,18,23)$ |
| $ 15, 15, 3 $ | $3168$ | $15$ | $( 1, 9,16, 4,20, 3, 8,18, 6,19, 2, 7,17, 5,21)(10,14,30,23,25,12,13,29,22,27, 11,15,28,24,26)(31,32,33)$ |
| $ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ | $1584$ | $5$ | $( 1, 8,17, 4,19)( 2, 9,18, 5,20)( 3, 7,16, 6,21)(10,13,28,23,27) (11,14,29,24,25)(12,15,30,22,26)$ |
| $ 10, 10, 5, 5, 2, 1 $ | $4752$ | $10$ | $( 1, 7,17, 6,19, 3, 8,16, 4,21)( 2, 9,18, 5,20)(10,14,28,24,27,11,13,29,23,25) (12,15,30,22,26)(31,32)$ |
Group invariants
| Order: | $47520=2^{5} \cdot 3^{3} \cdot 5 \cdot 11$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |