Properties

Label 33T19
Order \(3630\)
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 $t$ :  $19$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,24,17,9,27,13,7,29,14,2,23,22,6,30,20,5,31,15,8,28,19,10,26,18,4,32,21,11,25,12)(3,33,16), (1,18,31,11,20,27,7,17,33,2,16,24,4,12,32)(3,14,28,8,15,26,6,19,29,9,13,30,10,22,23)(5,21,25)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
5:  $C_5$
6:  $C_6$
10:  $C_{10}$
15:  $C_{15}$
30:  $C_{30}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T19 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 $ $30$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,19,15,22,18,14,21,17,13,20,16) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $30$ $11$ $(12,19,15,22,18,14,21,17,13,20,16)(23,28,33,27,32,26,31,25,30,24,29)$
$ 11, 11, 11 $ $30$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,15,18,21,13,16,19,22,14,17,20) (23,32,30,28,26,24,33,31,29,27,25)$
$ 11, 11, 11 $ $30$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,14,16,18,20,22,13,15,17,19,21) (23,33,32,31,30,29,28,27,26,25,24)$
$ 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 $ $121$ $5$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,17,15,16,21)(14,22,18,20,19) (23,33,28,25,32)(24,27,31,29,30)$
$ 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 $ $121$ $15$ $( 1,17,27, 7,14,23, 6,20,31, 8,19,26, 4,21,25)( 2,22,30, 5,15,28,10,18,32,11, 12,24, 9,13,29)( 3,16,33)$
$ 15, 15, 3 $ $121$ $15$ $( 1,13,31, 9,21,28, 5,17,24, 7,19,26, 6,18,25)( 2,14,32, 3,15,33, 8,20,27,11, 12,30, 4,16,23)(10,22,29)$
$ 15, 15, 3 $ $121$ $15$ $( 1,21,33, 9,16,32, 8,18,28, 4,15,23,10,14,25)( 2,19,26)( 3,17,30, 6,22,31, 7, 20,24,11,12,29, 5,13,27)$
$ 15, 15, 3 $ $121$ $15$ $( 1,15,25)( 2,18,23, 4,13,30,10,20,29, 6,19,26, 5,16,28)( 3,21,32, 7,22,24, 8, 14,33,11,12,27, 9,17,31)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,16,25)( 2,20,30)( 3,13,24)( 4,17,29)( 5,21,23)( 6,14,28)( 7,18,33) ( 8,22,27)( 9,15,32)(10,19,26)(11,12,31)$
$ 15, 15, 3 $ $121$ $15$ $( 1,27,14, 6,31,19, 4,25,17, 7,23,20, 8,26,21)( 2,30,15,10,32,12, 9,29,22, 5, 28,18,11,24,13)( 3,33,16)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $121$ $3$ $( 1,24,21)( 2,29,14)( 3,23,18)( 4,28,22)( 5,33,15)( 6,27,19)( 7,32,12) ( 8,26,16)( 9,31,20)(10,25,13)(11,30,17)$
$ 15, 15, 3 $ $121$ $15$ $( 1,30,13, 5,23,22, 6,24,16, 9,27,20, 7,25,21)( 2,31,18, 8,26,15, 4,33,17, 3, 32,12,11,29,19)(10,28,14)$
$ 15, 15, 3 $ $121$ $15$ $( 1,31,14, 4,32,12, 8,26,13, 6,29,18, 7,33,21)( 2,24,17, 9,30,16,11,27,22,10, 23,19, 5,25,15)( 3,28,20)$
$ 15, 15, 3 $ $121$ $15$ $( 1,29,20,11,31,22, 2,27,18, 9,24,15, 6,30,21)( 3,25,16, 7,28,19,10,33,13, 4, 23,14, 5,32,12)( 8,26,17)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 9,10, 7, 5,11, 4, 3, 6, 8)(13,20,21,18,16,22,15,14,17,19)(23,24,32,30,25, 29,28,31,33,27)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(13,18,15,19,21,22,17,20,16,14)(23,30,28,27,32, 29,33,24,25,31)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ $121$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,29) (24,28)(25,27)(30,33)(31,32)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(13,19,17,14,15,22,16,18,21,20)(23,27,33,31,28, 29,25,30,32,24)$
$ 10, 10, 10, 1, 1, 1 $ $121$ $10$ $( 2, 3, 5, 9, 6,11,10, 8, 4, 7)(13,14,16,20,17,22,21,19,15,18)(23,31,25,24,33, 29,32,27,28,30)$
$ 6, 6, 6, 6, 6, 3 $ $121$ $6$ $( 1,17,26, 4,16,30)( 2,13,31, 3,20,25)( 5,12,24,11,21,32)( 6,19,29,10,14,27) ( 7,15,23, 9,18,33)( 8,22,28)$
$ 30, 3 $ $121$ $30$ $( 1,13,27, 2,21,25,10,19,31, 8,14,24, 3,18,23, 7,17,26, 6,20,28, 9,22,33,11, 16,29, 5,12,30)( 4,15,32)$
$ 30, 3 $ $121$ $30$ $( 1,21,28, 7,13,24, 8,19,27,10,20,33, 3,22,23,11,15,25, 5,12,29, 4,17,26, 2, 16,31, 9,14,30)( 6,18,32)$
$ 30, 3 $ $121$ $30$ $( 1,15,33, 9,20,32,10,22,25, 6,14,31,11,13,29, 2,17,26, 5,12,27, 4,21,23, 8, 18,28, 3,19,30)( 7,16,24)$
$ 30, 3 $ $121$ $30$ $( 1,16,27, 5,12,31, 7,21,33, 8,20,23, 3,14,29, 6,22,32, 2,15,28,11,17,26,10, 18,25, 4,13,30)( 9,19,24)$
$ 30, 3 $ $121$ $30$ $( 1,27,20)( 2,29,18, 3,31,16, 5,24,12, 9,32,15, 6,26,21,11,25,22,10,23,13, 8, 30,17, 4,33,14, 7,28,19)$
$ 30, 3 $ $121$ $30$ $( 1,24,12, 7,33,19,10,32,17, 6,26,16, 4,23,21, 3,27,18, 8,29,22, 5,30,13, 9, 25,14,11,28,20)( 2,31,15)$
$ 30, 3 $ $121$ $30$ $( 1,30,21, 8,31,17, 2,27,22, 4,32,13, 7,23,16, 6,26,15,10,25,19, 5,29,14, 3, 24,12,11,33,20)( 9,28,18)$
$ 30, 3 $ $121$ $30$ $( 1,31,21, 7,25,18,11,32,16,10,33,22, 2,30,15, 4,28,14, 9,23,17, 5,27,19, 6, 26,13, 3,29,20)( 8,24,12)$
$ 6, 6, 6, 6, 6, 3 $ $121$ $6$ $( 1,29,19, 4,25,20)( 2,24,12, 3,30,16)( 5,31,13,11,23,15)( 6,26,17,10,28,22) ( 7,32,21, 9,33,18)( 8,27,14)$

Group invariants

Order:  $3630=2 \cdot 3 \cdot 5 \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.