Properties

Label 33T16
Order \(1815\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
5:  $C_5$
15:  $C_{15}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T16 x 3

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 $ $1$ $1$ $()$
$ 11, 11, 11 $ $15$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21) (23,31,28,25,33,30,27,24,32,29,26)$
$ 11, 11, 11 $ $15$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19) (23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $15$ $11$ $(12,19,15,22,18,14,21,17,13,20,16)(23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $15$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,21,19,17,15,13,22,20,18,16,14) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $15$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,16,20,13,17,21,14,18,22,15,19) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 11 $ $15$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,22,16,21,15,20,14,19,13,18) (23,31,28,25,33,30,27,24,32,29,26)$
$ 11, 11, 11 $ $15$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,22,21,20,19,18,17,16,15,14,13) (23,29,24,30,25,31,26,32,27,33,28)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $15$ $11$ $(12,15,18,21,13,16,19,22,14,17,20)(23,33,32,31,30,29,28,27,26,25,24)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $121$ $5$ $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(13,15,21,17,16)(14,18,19,22,20) (23,28,32,33,25)(24,31,30,27,29)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $121$ $5$ $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(13,21,16,15,17)(14,19,20,18,22) (23,32,25,28,33)(24,30,29,31,27)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $121$ $5$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,16,17,21,15)(14,20,22,19,18) (23,25,33,32,28)(24,29,27,30,31)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $121$ $5$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,17,15,16,21)(14,22,18,20,19) (23,33,28,25,32)(24,27,31,29,30)$
$ 15, 15, 3 $ $121$ $15$ $( 1,16,27, 8,13,33, 3,12,24, 5,19,32, 2,14,31)( 4,21,28, 9,22,26, 7,15,29,10, 20,30,11,18,23)( 6,17,25)$
$ 15, 15, 3 $ $121$ $15$ $( 1,13,25, 5,22,26, 8,15,24, 2,18,28, 3,12,31)( 4,17,23,10,14,30, 9,20,27,11, 19,33, 7,21,32)( 6,16,29)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,15,31)( 2,19,25)( 3,12,30)( 4,16,24)( 5,20,29)( 6,13,23)( 7,17,28) ( 8,21,33)( 9,14,27)(10,18,32)(11,22,26)$
$ 15, 15, 3 $ $121$ $15$ $( 1,17,33, 9,19,28,11,14,24, 6,21,23, 2,20,31)( 3,12,29, 4,15,27, 7,13,32, 5, 18,25,10,22,26)( 8,16,30)$
$ 15, 15, 3 $ $121$ $15$ $( 1,21,25, 4,13,28, 8,17,32, 6,15,30, 7,16,31)( 2,22,26, 9,18,33,11,20,24,10, 19,23, 5,14,29)( 3,12,27)$
$ 15, 15, 3 $ $121$ $15$ $( 1,27,13, 3,24,19, 2,31,16, 8,33,12, 5,32,14)( 4,28,22, 7,29,20,11,23,21, 9, 26,15,10,30,18)( 6,25,17)$
$ 15, 15, 3 $ $121$ $15$ $( 1,29,14)( 2,30,19, 4,32,18,10,27,15, 6,23,17, 5,33,12)( 3,31,13, 7,24,22, 8, 25,16,11,28,20, 9,26,21)$
$ 15, 15, 3 $ $121$ $15$ $( 1,24,20, 3,30,22,11,32,19,10,29,18, 6,28,14)( 2,27,21, 7,31,15, 5,25,13, 8, 23,16, 9,26,17)( 4,33,12)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,30,14)( 2,24,18)( 3,29,22)( 4,23,15)( 5,28,19)( 6,33,12)( 7,27,16) ( 8,32,20)( 9,26,13)(10,31,17)(11,25,21)$
$ 15, 15, 3 $ $121$ $15$ $( 1,31,21, 8,28,18, 5,23,13,11,33,12,10,24,14)( 2,29,19, 6,32,22, 9,26,16, 3, 27,17, 4,25,15)( 7,30,20)$

Group invariants

Order:  $1815=3 \cdot 5 \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1815, 3]
Character table: Data not available.