Properties

Label 33T12
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 $t$ :  $12$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,19,25)(2,12,30)(3,16,24)(4,20,29)(5,13,23)(6,17,28)(7,21,33)(8,14,27)(9,18,32)(10,22,26)(11,15,31), (1,25,18,5,27,12)(2,31,22,4,32,19)(3,26,15)(6,33,16,11,30,14)(7,28,20,10,24,21)(8,23,13,9,29,17)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
6:  $C_6$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T12 x 3

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 $ $6$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,21,19,17,15,13,22,20,18,16,14) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,19,15,22,18,14,21,17,13,20,16) (23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,15,18,21,13,16,19,22,14,17,20) (23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,18,13,19,14,20,15,21,16,22,17) (23,29,24,30,25,31,26,32,27,33,28)$
$ 11, 11, 11 $ $6$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,13,14,15,16,17,18,19,20,21,22) (23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,13,14,15,16,17,18,19,20,21,22)(23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22,21,20,19,18,17,16,15,14,13) (23,28,33,27,32,26,31,25,30,24,29)$
$ 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 $ $6$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21) (23,31,28,25,33,30,27,24,32,29,26)$
$ 11, 11, 11 $ $6$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,15,18,21,13,16,19,22,14,17,20) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,17,22,16,21,15,20,14,19,13,18)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,21,19,17,15,13,22,20,18,16,14) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(23,29,24,30,25,31,26,32,27,33,28)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $(12,14,16,18,20,22,13,15,17,19,21)(23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,21,19,17,15,13,22,20,18,16,14) (23,33,32,31,30,29,28,27,26,25,24)$
$ 11, 11, 11 $ $6$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19) (23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,18,13,19,14,20,15,21,16,22,17) (23,30,26,33,29,25,32,28,24,31,27)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,19,15,22,18,14,21,17,13,20,16) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 11 $ $6$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,15,18,21,13,16,19,22,14,17,20) (23,30,26,33,29,25,32,28,24,31,27)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,19,25)( 2,12,30)( 3,16,24)( 4,20,29)( 5,13,23)( 6,17,28)( 7,21,33) ( 8,14,27)( 9,18,32)(10,22,26)(11,15,31)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,25,19)( 2,30,12)( 3,24,16)( 4,29,20)( 5,23,13)( 6,28,17)( 7,33,21) ( 8,27,14)( 9,32,18)(10,26,22)(11,31,15)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,29) (24,28)(25,27)(30,33)(31,32)$
$ 6, 6, 6, 6, 6, 3 $ $121$ $6$ $( 1,19,24, 6,21,27)( 2,15,29, 5,14,33)( 3,22,23, 4,18,28)( 7,17,32,11,12,30) ( 8,13,26,10,16,25)( 9,20,31)$
$ 6, 6, 6, 6, 6, 3 $ $121$ $6$ $( 1,25,14, 7,28,16)( 2,31,18, 6,33,12)( 3,26,22, 5,27,19)( 4,32,15) ( 8,23,20,11,30,21)( 9,29,13,10,24,17)$

Group invariants

Order:  $726=2 \cdot 3 \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [726, 6]
Character table: Data not available.