# Properties

 Label 33T40 Order $$32736$$ n $$33$$ Cyclic No Abelian No Solvable No Primitive Yes $p$-group No Group: $\PSL(2,32)$

## 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

None

Resolvents shown for degrees $\leq 47$

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 $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $11, 11, 11$ $992$ $11$ $( 1, 5,32,19, 4,17,27,28,21, 2,29)( 3,18,12,30,13,31,25, 9,20, 6,23) ( 7,11,14,10,22,15,16,26, 8,24,33)$ $11, 11, 11$ $992$ $11$ $( 1,19,27, 2, 5, 4,28,29,32,17,21)( 3,30,25, 6,18,13, 9,23,12,31,20) ( 7,10,16,24,11,22,26,33,14,15, 8)$ $11, 11, 11$ $992$ $11$ $( 1, 2,28,17,19, 5,29,21,27, 4,32)( 3, 6, 9,31,30,18,23,20,25,13,12) ( 7,24,26,15,10,11,33, 8,16,22,14)$ $11, 11, 11$ $992$ $11$ $( 1,17,29, 4, 2,19,21,32,28, 5,27)( 3,31,23,13, 6,30,20,12, 9,18,25) ( 7,15,33,22,24,10, 8,14,26,11,16)$ $11, 11, 11$ $992$ $11$ $( 1, 4,21, 5,17, 2,32,27,29,19,28)( 3,13,20,18,31, 6,12,25,23,30, 9) ( 7,22, 8,11,15,24,14,16,33,10,26)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3$ $992$ $3$ $( 1, 8, 9)( 2,16,31)( 3, 4,11)( 5,24,20)( 6,32,33)( 7,23,19)(10,12,27) (13,21,15)(14,18,17)(22,30,28)(25,29,26)$ $33$ $992$ $33$ $( 1,13,14,32,25,22, 4,20,16,27,23, 8,21,18,33,29,30,11, 5,31,10,19, 9,15,17, 6,26,28, 3,24, 2,12, 7)$ $33$ $992$ $33$ $( 1,15,18,32,26,30, 4,24,31,27, 7, 9,21,14, 6,29,22, 3, 5,16,12,19, 8,13,17, 33,25,28,11,20, 2,10,23)$ $33$ $992$ $33$ $( 1,18,26, 4,31, 7,21, 6,22, 5,12, 8,17,25,11, 2,23,15,32,30,24,27, 9,14,29, 3,16,19,13,33,28,20,10)$ $33$ $992$ $33$ $( 1,14,25, 4,16,23,21,33,30, 5,10, 9,17,26, 3, 2, 7,13,32,22,20,27, 8,18,29, 11,31,19,15, 6,28,24,12)$ $33$ $992$ $33$ $( 1,25,16,21,30,10,17, 3, 7,32,20, 8,29,31,15,28,12,14, 4,23,33, 5, 9,26, 2, 13,22,27,18,11,19, 6,24)$ $33$ $992$ $33$ $( 1,26,31,21,22,12,17,11,23,32,24, 9,29,16,13,28,10,18, 4, 7, 6, 5, 8,25, 2, 15,30,27,14, 3,19,33,20)$ $33$ $992$ $33$ $( 1,31,22,17,23,24,29,13,10, 4, 6, 8, 2,30,14,19,20,26,21,12,11,32, 9,16,28, 18, 7, 5,25,15,27, 3,33)$ $33$ $992$ $33$ $( 1,16,30,17, 7,20,29,15,12, 4,33, 9, 2,22,18,19,24,25,21,10, 3,32, 8,31,28, 14,23, 5,26,13,27,11, 6)$ $33$ $992$ $33$ $( 1,30, 7,29,12,33, 2,18,24,21, 3, 8,28,23,26,27, 6,16,17,20,15, 4, 9,22,19, 25,10,32,31,14, 5,13,11)$ $33$ $992$ $33$ $( 1,22,23,29,10, 6, 2,14,20,21,11, 9,28, 7,25,27,33,31,17,24,13, 4, 8,30,19, 26,12,32,16,18, 5,15, 3)$ $31, 1, 1$ $1056$ $31$ $( 1, 6,16, 3,28,26,18,24,19, 4,32,11, 2,14,15,30, 8,21,10, 7, 9,13,27,23,22, 12,31,17,25, 5,29)$ $31, 1, 1$ $1056$ $31$ $( 1, 8, 6,21,16,10, 3, 7,28, 9,26,13,18,27,24,23,19,22, 4,12,32,31,11,17, 2, 25,14, 5,15,29,30)$ $31, 1, 1$ $1056$ $31$ $( 1,19, 8,22, 6, 4,21,12,16,32,10,31, 3,11, 7,17,28, 2, 9,25,26,14,13, 5,18, 15,27,29,24,30,23)$ $31, 1, 1$ $1056$ $31$ $( 1,28,19, 2, 8, 9,22,25, 6,26, 4,14,21,13,12, 5,16,18,32,15,10,27,31,29, 3, 24,11,30, 7,23,17)$ $31, 1, 1$ $1056$ $31$ $( 1,16,28,18,19,32, 2,15, 8,10, 9,27,22,31,25,29, 6, 3,26,24, 4,11,14,30,21, 7,13,23,12,17, 5)$ $31, 1, 1$ $1056$ $31$ $( 1,12, 7,14,24, 6,31, 9,15,19,16,17,13,30, 4, 3,25,27, 8,32,28, 5,23,21,11, 26,29,22,10, 2,18)$ $31, 1, 1$ $1056$ $31$ $( 1,25,12,27, 7, 8,14,32,24,28, 6, 5,31,23, 9,21,15,11,19,26,16,29,17,22,13, 10,30, 2, 4,18, 3)$ $31, 1, 1$ $1056$ $31$ $( 1,15,25,11,12,19,27,26, 7,16, 8,29,14,17,32,22,24,13,28,10, 6,30, 5, 2,31, 4,23,18, 9, 3,21)$ $31, 1, 1$ $1056$ $31$ $( 1,24,15,13,25,28,11,10,12, 6,19,30,27, 5,26, 2, 7,31,16, 4, 8,23,29,18,14, 9,17, 3,32,21,22)$ $31, 1, 1$ $1056$ $31$ $( 1, 7,24,31,15,16,13, 4,25, 8,28,23,11,29,10,18,12,14, 6, 9,19,17,30, 3,27, 32, 5,21,26,22, 2)$ $31, 1, 1$ $1056$ $31$ $( 1,26,32,30, 9,12,29,28, 4,15, 7,22, 5, 3,19,14,10,23,25,16,24, 2,21,27,17, 6,18,11, 8,13,31)$ $31, 1, 1$ $1056$ $31$ $( 1,10,26,23,32,25,30,16, 9,24,12, 2,29,21,28,27, 4,17,15, 6, 7,18,22,11, 5, 8, 3,13,19,31,14)$ $31, 1, 1$ $1056$ $31$ $( 1, 4,10,17,26,15,23, 6,32, 7,25,18,30,22,16,11, 9, 5,24, 8,12, 3, 2,13,29, 19,21,31,28,14,27)$ $31, 1, 1$ $1056$ $31$ $( 1, 9, 4, 5,10,24,17, 8,26,12,15, 3,23, 2, 6,13,32,29, 7,19,25,21,18,31,30, 28,22,14,16,27,11)$ $31, 1, 1$ $1056$ $31$ $( 1,32, 9,29, 4, 7, 5,19,10,25,24,21,17,18, 8,31,26,30,12,28,15,22, 3,14,23, 16, 2,27, 6,11,13)$ $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1$ $1023$ $2$ $( 1,26)( 2,31)( 3,11)( 4,25)( 5,15)( 6,29)( 7, 9)( 8,14)(10,22)(12,13)(16,23) (17,24)(18,30)(19,33)(21,32)(27,28)$

## 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.