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

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.