Properties

Label 33T17
Order \(1980\)
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 $t$ :  $17$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,24,5,14,8)(2,23,4,13,7)(3,22,6,15,9)(10,17,25,21,31)(11,16,26,19,33)(12,18,27,20,32), (1,22,26,8,10,19,5,30,33,18,15,2,24,25,7,12,21,4,28,31,16,14,3,23,27,9,11,20,6,29,32,17,13)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
660:  $\PSL(2,11)$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

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

Low degree siblings

33T17, 36T3021

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

Group invariants

Order:  $1980=2^{2} \cdot 3^{2} \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  [1980, 57]
Character table: Data not available.