Properties

Label 33T22
Order \(3960\)
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 $t$ :  $22$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8,28,21,4,3,7,30,20,5)(2,9,29,19,6)(10,23,32,15,18)(11,22,31,14,17,12,24,33,13,16)(25,26), (1,2)(4,15,20,6,13,19)(5,14,21)(7,18,31,9,17,32)(8,16,33)(10,24,27,11,23,25)(12,22,26)(28,29)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
660:  $\PSL(2,11)$
1320:  22T13

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: $\PSL(2,11)$

Low degree siblings

33T22, 36T4977

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

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 $ $2$ $3$ $( 1, 3, 2)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,18,17)(19,20,21) (22,23,24)(25,26,27)(28,30,29)(31,33,32)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $3$ $2$ $( 2, 3)( 5, 6)( 8, 9)(10,12)(14,15)(16,18)(19,21)(22,23)(26,27)(29,30)(32,33)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1 $ $110$ $3$ $( 4,24,13)( 5,22,14)( 6,23,15)(10,27,19)(11,25,20)(12,26,21)(16,33,30) (17,31,28)(18,32,29)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $220$ $3$ $( 1, 3, 2)( 4,22,15)( 5,23,13)( 6,24,14)( 7, 8, 9)(10,25,21)(11,26,19) (12,27,20)(16,32,28)(17,33,29)(18,31,30)$
$ 6, 6, 6, 3, 3, 3, 2, 2, 1, 1 $ $330$ $6$ $( 2, 3)( 4,24,13)( 5,23,14, 6,22,15)( 8, 9)(10,26,19,12,27,21)(11,25,20) (16,32,30,18,33,29)(17,31,28)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $55$ $2$ $( 4,28)( 5,30)( 6,29)(13,17)(14,16)(15,18)(19,27)(20,25)(21,26)(22,33)(23,32) (24,31)$
$ 6, 6, 6, 6, 3, 3, 3 $ $110$ $6$ $( 1, 3, 2)( 4,30, 6,28, 5,29)( 7, 8, 9)(10,11,12)(13,16,15,17,14,18) (19,25,21,27,20,26)(22,32,24,33,23,31)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ $165$ $2$ $( 2, 3)( 4,28)( 5,29)( 6,30)( 8, 9)(10,12)(13,17)(14,18)(15,16)(19,26)(20,25) (21,27)(22,32)(23,33)(24,31)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $132$ $5$ $( 4,17,24,31,25)( 5,16,22,33,26)( 6,18,23,32,27)( 7,28,11,20,13) ( 8,30,12,21,14)( 9,29,10,19,15)$
$ 15, 15, 3 $ $264$ $15$ $( 1, 3, 2)( 4,16,23,31,26, 6,17,22,32,25, 5,18,24,33,27)( 7,30,10,20,14, 9,28, 12,19,13, 8,29,11,21,15)$
$ 10, 10, 5, 5, 2, 1 $ $396$ $10$ $( 2, 3)( 4,17,24,31,25)( 5,18,22,32,26, 6,16,23,33,27)( 7,28,11,20,13) ( 8,29,12,19,14, 9,30,10,21,15)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $132$ $5$ $( 4, 7,28,25,20)( 5, 8,30,26,21)( 6, 9,29,27,19)(10,15,32,23,18) (11,13,31,24,17)(12,14,33,22,16)$
$ 15, 15, 3 $ $264$ $15$ $( 1, 3, 2)( 4, 8,29,25,21, 6, 7,30,27,20, 5, 9,28,26,19)(10,13,33,23,17,12,15, 31,22,18,11,14,32,24,16)$
$ 10, 10, 5, 5, 2, 1 $ $396$ $10$ $( 2, 3)( 4, 7,28,25,20)( 5, 9,30,27,21, 6, 8,29,26,19)(10,14,32,22,18,12,15, 33,23,16)(11,13,31,24,17)$
$ 6, 6, 6, 6, 3, 2, 2, 2 $ $330$ $6$ $( 1, 9)( 2, 7)( 3, 8)( 4,18,13,29,24,32)( 5,16,14,30,22,33)( 6,17,15,28,23,31) (10,25,19,11,27,20)(12,26,21)$
$ 6, 6, 6, 6, 3, 3, 3 $ $220$ $6$ $( 1, 8, 2, 7, 3, 9)( 4,16,15,28,22,32)( 5,18,13,30,23,31)( 6,17,14,29,24,33) (10,25,21)(11,26,19)(12,27,20)$
$ 6, 6, 6, 3, 3, 3, 2, 2, 2 $ $110$ $6$ $( 1, 7)( 2, 9)( 3, 8)( 4,17,13,28,24,31)( 5,16,14,30,22,33)( 6,18,15,29,23,32) (10,27,19)(11,25,20)(12,26,21)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 7,28,11,25, 4,31,20,24,17,13)( 2, 9,29,10,27, 6,32,19,23,18,15) ( 3, 8,30,12,26, 5,33,21,22,16,14)$
$ 33 $ $120$ $33$ $( 1, 8,29,11,26, 6,31,21,23,17,14, 2, 7,30,10,25, 5,32,20,22,18,13, 3, 9,28, 12,27, 4,33,19,24,16,15)$
$ 22, 11 $ $180$ $22$ $( 1, 7,28,11,25, 4,31,20,24,17,13)( 2, 8,29,12,27, 5,32,21,23,16,15, 3, 9,30, 10,26, 6,33,19,22,18,14)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 7,28,13,31,11, 4,17,20,25,24)( 2, 9,29,15,32,10, 6,18,19,27,23) ( 3, 8,30,14,33,12, 5,16,21,26,22)$
$ 33 $ $120$ $33$ $( 1, 8,29,13,33,10, 4,16,19,25,22, 2, 7,30,15,31,12, 6,17,21,27,24, 3, 9,28, 14,32,11, 5,18,20,26,23)$
$ 22, 11 $ $180$ $22$ $( 1, 7,28,13,31,11, 4,17,20,25,24)( 2, 8,29,14,32,12, 6,16,19,26,23, 3, 9,30, 15,33,10, 5,18,21,27,22)$

Group invariants

Order:  $3960=2^{3} \cdot 3^{2} \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.