Properties

Label 33T13
Order \(726\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $33$
Transitive number $t$ :  $13$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,19,3,16,5,13,7,21,9,18,11,15,2,12,4,20,6,17,8,14,10,22)(23,24,25,26,27,28,29,30,31,32,33), (1,9,6,3,11,8,5,2,10,7,4)(12,31,13,24,14,28,15,32,16,25,17,29,18,33,19,26,20,30,21,23,22,27)
$|\Aut(F/K)|$:  $11$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T14

Siblings are shown 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 $ $1$ $1$ $()$
$ 11, 11, 11 $ $3$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,20,17,14,22,19,16,13,21,18,15) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $3$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,17,22,16,21,15,20,14,19,13,18) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 11 $ $3$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,22,21,20,19,18,17,16,15,14,13) (23,31,28,25,33,30,27,24,32,29,26)$
$ 11, 11, 11 $ $3$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,21,19,17,15,13,22,20,18,16,14) (23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $3$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,19,15,22,18,14,21,17,13,20,16) (23,33,32,31,30,29,28,27,26,25,24)$
$ 11, 11, 11 $ $3$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,15,18,21,13,16,19,22,14,17,20) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 11 $ $3$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,18,13,19,14,20,15,21,16,22,17) (23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $3$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,13,14,15,16,17,18,19,20,21,22) (23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 11 $ $3$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,14,16,18,20,22,13,15,17,19,21) (23,29,24,30,25,31,26,32,27,33,28)$
$ 11, 11, 11 $ $3$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,16,20,13,17,21,14,18,22,15,19) (23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,21,19,17,15,13,22,20,18,16,14)(23,31,28,25,33,30,27,24,32,29,26)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,20,17,14,22,19,16,13,21,18,15) (23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,19,15,22,18,14,21,17,13,20,16) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $6$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,17,22,16,21,15,20,14,19,13,18) (23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $6$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,13,14,15,16,17,18,19,20,21,22) (23,29,24,30,25,31,26,32,27,33,28)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,16,20,13,17,21,14,18,22,15,19) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,22,21,20,19,18,17,16,15,14,13)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,14,16,18,20,22,13,15,17,19,21) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,19,15,22,18,14,21,17,13,20,16)(23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,17,22,16,21,15,20,14,19,13,18) (23,33,32,31,30,29,28,27,26,25,24)$
$ 11, 11, 11 $ $6$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,22,21,20,19,18,17,16,15,14,13) (23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,14,16,18,20,22,13,15,17,19,21) (23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,20,17,14,22,19,16,13,21,18,15) (23,31,28,25,33,30,27,24,32,29,26)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,15,18,21,13,16,19,22,14,17,20)(23,33,32,31,30,29,28,27,26,25,24)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,18,13,19,14,20,15,21,16,22,17)(23,32,30,28,26,24,33,31,29,27,25)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $242$ $3$ $( 1,16,29)( 2,20,23)( 3,13,28)( 4,17,33)( 5,21,27)( 6,14,32)( 7,18,26) ( 8,22,31)( 9,15,25)(10,19,30)(11,12,24)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $33$ $2$ $(12,24)(13,28)(14,32)(15,25)(16,29)(17,33)(18,26)(19,30)(20,23)(21,27)(22,31)$
$ 22, 11 $ $33$ $22$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,26,15,27,18,28,21,29,13,30,16,31,19,32, 22,33,14,23,17,24,20,25)$
$ 22, 11 $ $33$ $22$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,28,18,30,13,32,19,23,14,25,20,27,15,29, 21,31,16,33,22,24,17,26)$
$ 22, 11 $ $33$ $22$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,32,13,25,14,29,15,33,16,26,17,30,18,23, 19,27,20,31,21,24,22,28)$
$ 22, 11 $ $33$ $22$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,29,14,26,16,23,18,31,20,28,22,25,13,33, 15,30,17,27,19,24,21,32)$
$ 22, 11 $ $33$ $22$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,23,16,28,20,33,13,27,17,32,21,26,14,31, 18,25,22,30,15,24,19,29)$
$ 22, 11 $ $33$ $22$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,33,20,32,17,31,14,30,22,29,19,28,16,27, 13,26,21,25,18,24,15,23)$
$ 22, 11 $ $33$ $22$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,31,17,29,22,27,16,25,21,23,15,32,20,30, 14,28,19,26,13,24,18,33)$
$ 22, 11 $ $33$ $22$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,27,22,23,21,30,20,26,19,33,18,29,17,25, 16,32,15,28,14,24,13,31)$
$ 22, 11 $ $33$ $22$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,30,21,33,19,25,17,28,15,31,13,23,22,26, 20,29,18,32,16,24,14,27)$
$ 22, 11 $ $33$ $22$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,25,19,31,15,26,22,32,18,27,14,33,21,28, 17,23,13,29,20,24,16,30)$

Group invariants

Order:  $726=2 \cdot 3 \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [726, 5]
Character table: Data not available.