Properties

Label 33T40
Degree $33$
Order $32736$
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)
$|\Aut(F/K)|$:  $1$
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)

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

Group invariants

Order:  $32736=2^{5} \cdot 3 \cdot 11 \cdot 31$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.