Group action invariants
| Degree $n$ : | $33$ | |
| Transitive number $t$ : | $40$ | |
| Group : | $\PSL(2,32)$ | |
| Parity: | $1$ | |
| Primitive: | Yes | |
| Nilpotency class: | $-1$ (not nilpotent) | |
| Generators: | (1,32)(2,19)(3,6)(4,30)(5,11)(7,28)(8,23)(9,21)(10,17)(12,20)(13,24)(14,15)(16,25)(18,31)(22,26)(27,29), (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), (2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(32,33) | |
| $|\Aut(F/K)|$: | $1$ |
Low degree resolvents
NoneResolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 11: None
Low degree siblings
There are no siblings 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 $ | $992$ | $11$ | $( 1, 7,30,26, 4,16,28, 6, 2,25,31)( 3,27,17,12,32,13,10, 9,14,21,24) ( 5,29, 8,11,18,23,22,19,33,20,15)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1,26,28,25, 7, 4, 6,31,30,16, 2)( 3,12,10,21,27,32, 9,24,17,13,14) ( 5,11,22,20,29,18,19,15, 8,23,33)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1,25, 6,16,26, 7,31, 2,28, 4,30)( 3,21, 9,13,12,27,24,14,10,32,17) ( 5,20,19,23,11,29,15,33,22,18, 8)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1,16,31, 4,25,26, 2,30, 6, 7,28)( 3,13,24,32,21,12,14,17, 9,27,10) ( 5,23,15,18,20,11,33, 8,19,29,22)$ |
| $ 11, 11, 11 $ | $992$ | $11$ | $( 1, 4, 2, 7,16,25,30,28,31,26, 6)( 3,32,14,27,13,21,17,10,24,12, 9) ( 5,18,33,29,23,20, 8,22,15,11,19)$ |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $992$ | $3$ | $( 1,22, 9)( 2,11,32)( 3, 4,15)( 5,27,16)( 6, 8,12)( 7,19,14)(10,31,23) (13,25,18)(17,28,29)(20,24,26)(21,30,33)$ |
| $ 33 $ | $992$ | $33$ | $( 1, 3,11, 7,27,18,30,17,23,26,12,22, 4,32,19,16,13,33,28,10,20, 6, 9,15, 2, 14, 5,25,21,29,31,24, 8)$ |
| $ 33 $ | $992$ | $33$ | $( 1,15,32, 7, 5,13,30,29,10,26, 8, 9, 4,11,14,16,18,21,28,23,24, 6,22, 3, 2, 19,27,25,33,17,31,20,12)$ |
| $ 33 $ | $992$ | $33$ | $( 1,32, 5,30,10, 8, 4,14,18,28,24,22, 2,27,33,31,12,15, 7,13,29,26, 9,11,16, 21,23, 6, 3,19,25,17,20)$ |
| $ 33 $ | $992$ | $33$ | $( 1,11,27,30,23,12, 4,19,13,28,20, 9, 2, 5,21,31, 8, 3, 7,18,17,26,22,32,16, 33,10, 6,15,14,25,29,24)$ |
| $ 33 $ | $992$ | $33$ | $( 1,27,23, 4,13,20, 2,21, 8, 7,17,22,16,10,15,25,24,11,30,12,19,28, 9, 5,31, 3,18,26,32,33, 6,14,29)$ |
| $ 33 $ | $992$ | $33$ | $( 1, 5,10, 4,18,24, 2,33,12, 7,29, 9,16,23, 3,25,20,32,30, 8,14,28,22,27,31, 15,13,26,11,21, 6,19,17)$ |
| $ 33 $ | $992$ | $33$ | $( 1,10,18, 2,12,29,16, 3,20,30,14,22,31,13,11, 6,17, 5, 4,24,33, 7, 9,23,25, 32, 8,28,27,15,26,21,19)$ |
| $ 33 $ | $992$ | $33$ | $( 1,23,13, 2, 8,17,16,15,24,30,19, 9,31,18,32, 6,29,27, 4,20,21, 7,22,10,25, 11,12,28, 5, 3,26,33,14)$ |
| $ 33 $ | $992$ | $33$ | $( 1,13, 8,16,24,19,31,32,29, 4,21,22,25,12, 5,26,14,23, 2,17,15,30, 9,18, 6, 27,20, 7,10,11,28, 3,33)$ |
| $ 33 $ | $992$ | $33$ | $( 1,18,12,16,20,14,31,11,17, 4,33, 9,25, 8,27,26,19,10, 2,29, 3,30,22,13, 6, 5,24, 7,23,32,28,15,21)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,15,17, 9,20, 5,29, 7,22, 8, 3, 6,32,19,31,10,23, 2,14,33,27,30,25,11,26, 4,28,13,24,16,18)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,23,15, 2,17,14, 9,33,20,27, 5,30,29,25, 7,11,22,26, 8, 4, 3,28, 6,13,32, 24,19,16,31,18,10)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,22,23,26,15, 8, 2, 4,17, 3,14,28, 9, 6,33,13,20,32,27,24, 5,19,30,16,29, 31,25,18, 7,10,11)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,20,22,32,23,27,26,24,15, 5, 8,19, 2,30, 4,16,17,29, 3,31,14,25,28,18, 9, 7, 6,10,33,11,13)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,17,20,29,22, 3,32,31,23,14,27,25,26,28,24,18,15, 9, 5, 7, 8, 6,19,10, 2, 33,30,11, 4,13,16)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 4,33,19, 7,15,28,27,31,22,17,13,30,10, 8, 9,24,25,23, 3,20,16,11, 2, 6, 5,18,26,14,32,29)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,24, 4,25,33,23,19, 3, 7,20,15,16,28,11,27, 2,31, 6,22, 5,17,18,13,26,30, 14,10,32, 8,29, 9)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,31,24, 6, 4,22,25, 5,33,17,23,18,19,13, 3,26, 7,30,20,14,15,10,16,32,28, 8,11,29,27, 9, 2)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 7,31,30,24,20, 6,14, 4,15,22,10,25,16, 5,32,33,28,17, 8,23,11,18,29,19, 27,13, 9, 3, 2,26)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,33, 7,28,31,17,30, 8,24,23,20,11, 6,18,14,29, 4,19,15,27,22,13,10, 9,25, 3,16, 2, 5,26,32)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 5, 3,10,27, 4,18,20, 8,31,33,26,16, 9,22,19,14,11,24,17, 7,32, 2,25,13, 15,29, 6,23,30,28)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,14, 5,11, 3,24,10,17,27, 7, 4,32,18, 2,20,25, 8,13,31,15,33,29,26, 6,16, 23, 9,30,22,28,19)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 8,14,13, 5,31,11,15, 3,33,24,29,10,26,17, 6,27,16, 7,23, 4, 9,32,30,18, 22, 2,28,20,19,25)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1,27, 8,16,14, 7,13,23, 5, 4,31, 9,11,32,15,30, 3,18,33,22,24, 2,29,28,10, 20,26,19,17,25, 6)$ |
| $ 31, 1, 1 $ | $1056$ | $31$ | $( 1, 3,27,18, 8,33,16,22,14,24, 7, 2,13,29,23,28, 5,10, 4,20,31,26, 9,19,11, 17,32,25,15, 6,30)$ |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ | $1023$ | $2$ | $( 1,30)( 2, 9)( 3,13)( 4,29)( 5,24)( 6,16)( 7,33)( 8,31)(10,17)(11,19)(12,32) (14,26)(15,21)(18,20)(22,23)(27,28)$ |
Group invariants
| Order: | $32736=2^{5} \cdot 3 \cdot 11 \cdot 31$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | No | |
| GAP id: | Data not available |
| Character table: Data not available. |