Properties

Label 33T35
Degree $33$
Order $23760$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

Learn more about

Group action invariants

Degree $n$:  $33$
Transitive number $t$:  $35$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $3$
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)

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

Group invariants

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