Properties

Label 33T35
Order \(23760\)
n \(33\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $33$
Transitive number $t$ :  $35$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,23,30,25,4,2,24,28,26,5,3,22,29,27,6)(7,16,21,33,11,8,17,19,31,12,9,18,20,32,10)(13,15,14), (4,28,20,14)(5,29,21,15)(6,30,19,13)(7,17,23,27)(8,18,24,25)(9,16,22,26)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
7920:  $M_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: $M_{11}$

Low degree siblings

36T12768

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 $ $1$ $1$ $()$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)(28,29,30)(31,32,33)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20) (22,24,23)(25,27,26)(28,30,29)(31,33,32)$
$ 33 $ $720$ $33$ $( 1, 6,27,15,32,23,21, 9,17,10,30, 3, 5,26,14,31,22,20, 8,16,12,29, 2, 4,25, 13,33,24,19, 7,18,11,28)$
$ 33 $ $720$ $33$ $( 1, 4,26,15,33,22,21, 7,16,10,28, 2, 5,27,13,31,23,19, 8,17,11,29, 3, 6,25, 14,32,24,20, 9,18,12,30)$
$ 11, 11, 11 $ $720$ $11$ $( 1, 5,25,15,31,24,21, 8,18,10,29)( 2, 6,26,13,32,22,19, 9,16,11,30) ( 3, 4,27,14,33,23,20, 7,17,12,28)$
$ 33 $ $720$ $33$ $( 1,30,12,18, 9,20,24,32,14,25, 6, 3,29,11,17, 8,19,23,31,13,27, 5, 2,28,10, 16, 7,21,22,33,15,26, 4)$
$ 33 $ $720$ $33$ $( 1,28,11,18, 7,19,24,33,13,25, 4, 2,29,12,16, 8,20,22,31,14,26, 5, 3,30,10, 17, 9,21,23,32,15,27, 6)$
$ 11, 11, 11 $ $720$ $11$ $( 1,29,10,18, 8,21,24,31,15,25, 5)( 2,30,11,16, 9,19,22,32,13,26, 6) ( 3,28,12,17, 7,20,23,33,14,27, 4)$
$ 15, 15, 3 $ $1584$ $15$ $( 1,13,23,31,19, 3,15,22,33,21, 2,14,24,32,20)( 4,18, 9,12,25, 6,17, 8,11,27, 5,16, 7,10,26)(28,29,30)$
$ 15, 15, 3 $ $1584$ $15$ $( 1,14,22,31,20, 2,15,23,32,21, 3,13,24,33,19)( 4,16, 8,12,26, 5,17, 9,10,27, 6,18, 7,11,25)(28,30,29)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $1584$ $5$ $( 1,15,24,31,21)( 2,13,22,32,19)( 3,14,23,33,20)( 4,17, 7,12,27) ( 5,18, 8,10,25)( 6,16, 9,11,26)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $440$ $3$ $( 1,22, 7)( 2,23, 8)( 3,24, 9)( 4,18,30)( 5,16,28)( 6,17,29)(10,11,12) (13,27,21)(14,25,19)(15,26,20)(31,32,33)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $440$ $3$ $( 1,23, 9)( 2,24, 7)( 3,22, 8)( 4,16,29)( 5,17,30)( 6,18,28)(10,12,11) (13,25,20)(14,26,21)(15,27,19)(31,33,32)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $440$ $3$ $( 1,24, 8)( 2,22, 9)( 3,23, 7)( 4,17,28)( 5,18,29)( 6,16,30)(13,26,19) (14,27,20)(15,25,21)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $165$ $2$ $( 1,25)( 2,26)( 3,27)( 7,14)( 8,15)( 9,13)(10,31)(11,32)(12,33)(19,22)(20,23) (21,24)$
$ 6, 6, 6, 6, 3, 3, 3 $ $165$ $6$ $( 1,26, 3,25, 2,27)( 4, 5, 6)( 7,15, 9,14, 8,13)(10,32,12,31,11,33)(16,17,18) (19,23,21,22,20,24)(28,29,30)$
$ 6, 6, 6, 6, 3, 3, 3 $ $165$ $6$ $( 1,27, 2,25, 3,26)( 4, 6, 5)( 7,13, 8,14, 9,15)(10,33,11,31,12,32)(16,18,17) (19,24,20,22,21,23)(28,30,29)$
$ 6, 6, 6, 6, 3, 3, 3 $ $1320$ $6$ $( 1,19, 7,25,22,14)( 2,20, 8,26,23,15)( 3,21, 9,27,24,13)( 4,18,30)( 5,16,28) ( 6,17,29)(10,32,12,31,11,33)$
$ 6, 6, 6, 6, 3, 3, 3 $ $1320$ $6$ $( 1,20, 9,25,23,13)( 2,21, 7,26,24,14)( 3,19, 8,27,22,15)( 4,16,29)( 5,17,30) ( 6,18,28)(10,33,11,31,12,32)$
$ 6, 6, 6, 3, 3, 3, 2, 2, 2 $ $1320$ $6$ $( 1,21, 8,25,24,15)( 2,19, 9,26,22,13)( 3,20, 7,27,23,14)( 4,17,28)( 5,18,29) ( 6,16,30)(10,31)(11,32)(12,33)$
$ 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $990$ $4$ $( 1,24,18,29)( 2,22,16,30)( 3,23,17,28)( 4,12, 7,33)( 5,10, 8,31)( 6,11, 9,32)$
$ 12, 12, 3, 3, 3 $ $990$ $12$ $( 1,22,17,29, 2,23,18,30, 3,24,16,28)( 4,10, 9,33, 5,11, 7,31, 6,12, 8,32) (13,14,15)(19,20,21)(25,26,27)$
$ 12, 12, 3, 3, 3 $ $990$ $12$ $( 1,23,16,29, 3,22,18,28, 2,24,17,30)( 4,11, 8,33, 6,10, 7,32, 5,12, 9,31) (13,15,14)(19,21,20)(25,27,26)$
$ 8, 8, 8, 2, 2, 2, 1, 1, 1 $ $990$ $8$ $( 1,31,24, 5,18,10,29, 8)( 2,32,22, 6,16,11,30, 9)( 3,33,23, 4,17,12,28, 7) (19,26)(20,27)(21,25)$
$ 24, 6, 3 $ $990$ $24$ $( 1,32,23, 5,16,12,29, 9, 3,31,22, 4,18,11,28, 8, 2,33,24, 6,17,10,30, 7) (13,14,15)(19,27,21,26,20,25)$
$ 24, 6, 3 $ $990$ $24$ $( 1,33,22, 5,17,11,29, 7, 2,31,23, 6,18,12,30, 8, 3,32,24, 4,16,10,28, 9) (13,15,14)(19,25,20,26,21,27)$
$ 8, 8, 8, 2, 2, 2, 1, 1, 1 $ $990$ $8$ $( 1, 8,29,10,18, 5,24,31)( 2, 9,30,11,16, 6,22,32)( 3, 7,28,12,17, 4,23,33) (19,26)(20,27)(21,25)$
$ 24, 6, 3 $ $990$ $24$ $( 1, 9,28,10,16, 4,24,32, 3, 8,30,12,18, 6,23,31, 2, 7,29,11,17, 5,22,33) (13,14,15)(19,27,21,26,20,25)$
$ 24, 6, 3 $ $990$ $24$ $( 1, 7,30,10,17, 6,24,33, 2, 8,28,11,18, 4,22,31, 3, 9,29,12,16, 5,23,32) (13,15,14)(19,25,20,26,21,27)$

Group invariants

Order:  $23760=2^{4} \cdot 3^{3} \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.