# Properties

 Label 33T18 Degree $33$ Order $2673$ Cyclic no Abelian no Solvable yes Primitive no $p$-group no

## Group action invariants

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

## Low degree resolvents

|G/N|Galois groups for stem field(s)
$11$:  $C_{11}$

Resolvents shown for degrees $\leq 47$

## Subfields

Degree 3: None

Degree 11: $C_{11}$

## Low degree siblings

33T18 x 10

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

## Conjugacy classes

 Cycle Type Size Order Representative $1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $1$ $1$ $()$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 4, 6, 5)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(22,24,23) (25,26,27)(28,29,30)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 3, 2)( 4, 5, 6)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24) (25,27,26)(28,30,29)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 4, 5, 6)( 7, 8, 9)(13,15,14)(19,20,21)(22,24,23)(31,33,32)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 7, 8, 9)(10,12,11)(13,14,15)(16,18,17)(22,23,24)(25,26,27) (28,29,30)(31,33,32)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 4, 6, 5)( 7, 9, 8)(13,14,15)(19,21,20)(22,23,24)(31,32,33)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 3, 2)( 7, 9, 8)(10,11,12)(13,15,14)(16,17,18)(22,24,23)(25,27,26) (28,30,29)(31,32,33)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $(10,11,12)(16,17,18)(19,21,20)(22,24,23)(25,27,26)(28,29,30)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 3, 2)( 4, 5, 6)(10,12,11)(13,14,15)(16,18,17)(25,26,27)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 7, 8, 9)(13,14,15)(19,21,20)(28,30,29)(31,33,32)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 4, 6, 5)( 7, 9, 8)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(25,27,26) (28,29,30)(31,32,33)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 4, 5, 6)( 7, 9, 8)(22,24,23)(28,30,29)(31,32,33)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 4, 6, 5)(10,11,12)(13,15,14)(16,17,18)(25,27,26)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 4, 5, 6)( 7, 8, 9)(10,12,11)(13,15,14)(16,18,17)(19,21,20)(25,26,27) (28,30,29)(31,33,32)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 3, 2)( 7, 9, 8)(13,15,14)(19,20,21)(28,29,30)(31,32,33)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 4, 6, 5)( 7, 8, 9)(10,12,11)(13,15,14)(16,17,18)(22,24,23) (28,30,29)(31,33,32)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 7, 8, 9)(10,11,12)(22,24,23)(25,26,27)(28,30,29)(31,33,32)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 3, 2)( 4, 5, 6)( 7, 8, 9)(10,12,11)(13,14,15)(16,17,18)(19,20,21) (28,29,30)(31,33,32)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 4, 6, 5)( 7, 8, 9)(10,11,12)(13,15,14)(19,20,21)(25,26,27) (28,29,30)(31,33,32)$ $3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(16,18,17)(19,20,21)(22,23,24)(25,27,26) (28,30,29)(31,32,33)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 2, 3)( 4, 5, 6)(10,11,12)(22,23,24)(25,26,27)(28,29,30)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 1, 3, 2)(13,15,14)(16,18,17)(19,21,20)(25,27,26)(28,30,29)$ $3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1$ $11$ $3$ $( 7, 9, 8)(10,12,11)(22,23,24)(25,27,26)(28,29,30)(31,32,33)$ $11, 11, 11$ $243$ $11$ $( 1,17,33,14,28,11,25, 8,22, 5,20)( 2,18,31,15,29,12,26, 9,23, 6,21) ( 3,16,32,13,30,10,27, 7,24, 4,19)$ $11, 11, 11$ $243$ $11$ $( 1,33,28,25,22,20,17,14,11, 8, 5)( 2,31,29,26,23,21,18,15,12, 9, 6) ( 3,32,30,27,24,19,16,13,10, 7, 4)$ $11, 11, 11$ $243$ $11$ $( 1,28,22,17,11, 5,33,25,20,14, 8)( 2,29,23,18,12, 6,31,26,21,15, 9) ( 3,30,24,16,10, 4,32,27,19,13, 7)$ $11, 11, 11$ $243$ $11$ $( 1,22,11,33,20, 8,28,17, 5,25,14)( 2,23,12,31,21, 9,29,18, 6,26,15) ( 3,24,10,32,19, 7,30,16, 4,27,13)$ $11, 11, 11$ $243$ $11$ $( 1,11,20,28, 5,14,22,33, 8,17,25)( 2,12,21,29, 6,15,23,31, 9,18,26) ( 3,10,19,30, 4,13,24,32, 7,16,27)$ $11, 11, 11$ $243$ $11$ $( 1,20, 5,22, 8,25,11,28,14,33,17)( 2,21, 6,23, 9,26,12,29,15,31,18) ( 3,19, 4,24, 7,27,10,30,13,32,16)$ $11, 11, 11$ $243$ $11$ $( 1, 5, 8,11,14,17,20,22,25,28,33)( 2, 6, 9,12,15,18,21,23,26,29,31) ( 3, 4, 7,10,13,16,19,24,27,30,32)$ $11, 11, 11$ $243$ $11$ $( 1, 8,14,20,25,33, 5,11,17,22,28)( 2, 9,15,21,26,31, 6,12,18,23,29) ( 3, 7,13,19,27,32, 4,10,16,24,30)$ $11, 11, 11$ $243$ $11$ $( 1,14,25, 5,17,28, 8,20,33,11,22)( 2,15,26, 6,18,29, 9,21,31,12,23) ( 3,13,27, 4,16,30, 7,19,32,10,24)$ $11, 11, 11$ $243$ $11$ $( 1,25,17, 8,33,22,14, 5,28,20,11)( 2,26,18, 9,31,23,15, 6,29,21,12) ( 3,27,16, 7,32,24,13, 4,30,19,10)$

## Group invariants

 Order: $2673=3^{5} \cdot 11$ Cyclic: no Abelian: no Solvable: yes GAP id: [2673, 68]
 Character table: not available.