Properties

Label 33T25
Order \(7260\)
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 $t$ :  $25$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,14,33,6,16,25)(2,21,27,5,20,31)(3,17,32,4,13,26)(7,12,30,11,18,28)(8,19,24,10,22,23)(9,15,29), (1,12,10,13,11,18,5,21,8,14)(2,17,4,16,3,22,9,19,6,15)(7,20)(23,24,28,33,31)(25,32,27,29,26)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
5:  $C_5$
6:  $S_3$
10:  $C_{10}$ x 3
12:  $D_{6}$
20:  20T3
30:  $S_3 \times C_5$
60:  30T12

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T25

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 $ $60$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,22,21,20,19,18,17,16,15,14,13) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $30$ $11$ $(12,20,17,14,22,19,16,13,21,18,15)(23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 11 $ $30$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,19,15,22,18,14,21,17,13,20,16) (23,33,32,31,30,29,28,27,26,25,24)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $242$ $3$ $( 1,33,16)( 2,27,20)( 3,32,13)( 4,26,17)( 5,31,21)( 6,25,14)( 7,30,18) ( 8,24,22)( 9,29,15)(10,23,19)(11,28,12)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,29) (24,28)(25,27)(30,33)(31,32)$
$ 6, 6, 6, 6, 6, 3 $ $242$ $6$ $( 1,33,18, 4,29,19)( 2,28,22, 3,23,15)( 5,24,12,11,27,14)( 6,30,16,10,32,21) ( 7,25,20, 9,26,17)( 8,31,13)$
$ 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 $ $242$ $15$ $( 1,33,12,11,30,22, 7,29,18, 2,25,13, 4,31,15)( 3,28,14, 8,32,19, 6,26,17, 9, 24,20,10,27,21)( 5,23,16)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(13,18,15,19,21,22,17,20,16,14)(23,30,28,27,32, 29,33,24,25,31)$
$ 30, 3 $ $242$ $30$ $( 1,33,22, 4,24,14, 3,27,13, 7,26,17, 2,30,12,11,25,21, 8,23,18, 9,31,19, 5, 32,15,10,28,20)( 6,29,16)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $121$ $5$ $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(13,15,21,17,16)(14,18,19,22,20) (23,28,32,33,25)(24,31,30,27,29)$
$ 15, 15, 3 $ $242$ $15$ $( 1,33,14, 7,24,21, 4,23,12,11,29,22, 2,26,17)( 3,30,20, 6,31,18,10,25,19, 8, 28,13, 9,32,16)( 5,27,15)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 9,10, 7, 5,11, 4, 3, 6, 8)(13,20,21,18,16,22,15,14,17,19)(23,24,32,30,25, 29,28,31,33,27)$
$ 30, 3 $ $242$ $30$ $( 1,33,20, 5,28,21, 7,31,16, 8,27,19, 3,25,15, 6,24,13, 2,29,12,11,26,17,10, 30,14, 4,32,18)( 9,23,22)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $121$ $5$ $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(13,21,16,15,17)(14,19,20,18,22) (23,32,25,28,33)(24,30,29,31,27)$
$ 15, 15, 3 $ $242$ $15$ $( 1,33,19, 2,23,13, 5,26,17, 3,24,18, 8,29,21)( 4,25,12,11,32,14,10,31,20, 7, 28,16, 9,30,15)( 6,27,22)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 3, 5, 9, 6,11,10, 8, 4, 7)(13,14,16,20,17,22,21,19,15,18)(23,31,25,24,33, 29,32,27,28,30)$
$ 30, 3 $ $242$ $30$ $( 1,33,15, 7,27,12,11,23,21,10,24,16, 2,32,20, 4,30,19, 9,25,22, 5,29,13, 6, 28,18, 3,31,14)( 8,26,17)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $121$ $5$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,16,17,21,15)(14,20,22,19,18) (23,25,33,32,28)(24,29,27,30,31)$
$ 15, 15, 3 $ $242$ $15$ $( 1,33,13)( 2,31,22,10,26,17, 5,25,16, 4,27,18, 6,23,14)( 3,29,20, 8,30,21, 9, 28,19, 7,32,12,11,24,15)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(13,19,17,14,15,22,16,18,21,20)(23,27,33,31,28, 29,25,30,32,24)$
$ 30, 3 $ $242$ $30$ $( 1,33,21, 2,24,19, 4,28,15, 8,25,18, 5,30,13,10,29,14, 9,27,16, 7,23,20, 3, 26,17, 6,32,22)(11,31,12)$
$ 10, 10, 5, 5, 2, 1 $ $363$ $10$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(12,25,14,24,13,30,19,27,16,23) (15,29,18,33,22,31,20,32,21,26)(17,28)$
$ 10, 10, 10, 2, 1 $ $363$ $10$ $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(12,27,19,25,21,26,20,31,15,23)(13,33) (14,28,18,30,16,29,17,24,22,32)$
$ 10, 10, 5, 5, 2, 1 $ $363$ $10$ $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(12,32,13,24,17,25,22,29,20,23) (14,27,21,26,16,33,18,28,15,30)(19,31)$
$ 10, 10, 10, 2, 1 $ $363$ $10$ $( 2, 3, 5, 9, 6,11,10, 8, 4, 7)(12,31,16,30,21,26,19,32,22,23)(13,28,20,29,15, 33,17,27,14,25)(18,24)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $33$ $2$ $(12,23)(13,27)(14,31)(15,24)(16,28)(17,32)(18,25)(19,29)(20,33)(21,26)(22,30)$
$ 22, 11 $ $330$ $22$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,32,16,26,20,31,13,25,17,30,21,24,14,29, 18,23,22,28,15,33,19,27)$
$ 22, 2, 2, 2, 2, 2, 1 $ $330$ $22$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,29,16,24,20,30,13,25,17,31,21,26,14,32, 18,27,22,33,15,28,19,23)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ $33$ $2$ $( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)(12,24)(13,31)(14,27)(15,23)(16,30)(17,26) (18,33)(19,29)(20,25)(21,32)(22,28)$
$ 10, 10, 5, 5, 2, 1 $ $363$ $10$ $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(12,28,13,29,22,27,15,31,18,23) (14,30,20,25,19,24,21,26,17,33)(16,32)$
$ 10, 10, 10, 2, 1 $ $363$ $10$ $( 2, 9,10, 7, 5,11, 4, 3, 6, 8)(12,24,14,33,21,26,18,29,13,23)(15,32,19,28,22, 25,16,31,17,30)(20,27)$
$ 10, 10, 5, 5, 2, 1 $ $363$ $10$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(12,33,19,30,18,32,15,27,17,23) (13,31,22,24,16,25,20,28,21,26)(14,29)$
$ 10, 10, 10, 2, 1 $ $363$ $10$ $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(12,30,17,29,21,26,22,28,14,23)(13,32,20,24,19, 33,16,27,18,31)(15,25)$

Group invariants

Order:  $7260=2^{2} \cdot 3 \cdot 5 \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.