Properties

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

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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 $\leq 47$

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

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.