Properties

Label 33T8
Order \(330\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_3\times F_{11}$

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Group action invariants

Degree $n$ :  $33$
Transitive number $t$ :  $8$
Group :  $C_3\times F_{11}$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,28)(2,29)(3,30)(4,26)(5,27)(6,25)(7,22)(8,23)(9,24)(10,21)(11,19)(12,20)(13,16)(14,17)(15,18), (1,7,5,23,13,2,8,6,24,14,3,9,4,22,15)(10,20,32,26,30,11,21,33,27,28,12,19,31,25,29)(16,18,17)
$|\Aut(F/K)|$:  $3$

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:  $C_{30}$
110:  $F_{11}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: $F_{11}$

Low degree siblings

There are no siblings 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 $ $1$ $1$ $()$
$ 10, 10, 10, 1, 1, 1 $ $11$ $10$ $( 4, 8,14,26,17,31,28,23,10,21)( 5, 9,15,27,18,32,29,24,11,19)( 6, 7,13,25,16, 33,30,22,12,20)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $11$ $5$ $( 4,10,28,17,14)( 5,11,29,18,15)( 6,12,30,16,13)( 7,20,22,33,25) ( 8,21,23,31,26)( 9,19,24,32,27)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $11$ $5$ $( 4,14,17,28,10)( 5,15,18,29,11)( 6,13,16,30,12)( 7,25,33,22,20) ( 8,26,31,23,21)( 9,27,32,24,19)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $11$ $5$ $( 4,17,10,14,28)( 5,18,11,15,29)( 6,16,12,13,30)( 7,33,20,25,22) ( 8,31,21,26,23)( 9,32,19,27,24)$
$ 10, 10, 10, 1, 1, 1 $ $11$ $10$ $( 4,21,10,23,28,31,17,26,14, 8)( 5,19,11,24,29,32,18,27,15, 9)( 6,20,12,22,30, 33,16,25,13, 7)$
$ 10, 10, 10, 1, 1, 1 $ $11$ $10$ $( 4,23,17, 8,10,31,14,21,28,26)( 5,24,18, 9,11,32,15,19,29,27)( 6,22,16, 7,12, 33,13,20,30,25)$
$ 10, 10, 10, 1, 1, 1 $ $11$ $10$ $( 4,26,28,21,14,31,10, 8,17,23)( 5,27,29,19,15,32,11, 9,18,24)( 6,25,30,20,13, 33,12, 7,16,22)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $11$ $5$ $( 4,28,14,10,17)( 5,29,15,11,18)( 6,30,13,12,16)( 7,22,25,20,33) ( 8,23,26,21,31)( 9,24,27,19,32)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ $11$ $2$ $( 4,31)( 5,32)( 6,33)( 7,30)( 8,28)( 9,29)(10,26)(11,27)(12,25)(13,22)(14,23) (15,24)(16,20)(17,21)(18,19)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)(28,29,30)(31,32,33)$
$ 30, 3 $ $11$ $30$ $( 1, 2, 3)( 4, 9,13,26,18,33,28,24,12,21, 5, 7,14,27,16,31,29,22,10,19, 6, 8, 15,25,17,32,30,23,11,20)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 2, 3)( 4,11,30,17,15, 6,10,29,16,14, 5,12,28,18,13)( 7,21,24,33,26, 9,20, 23,32,25, 8,19,22,31,27)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 2, 3)( 4,15,16,28,11, 6,14,18,30,10, 5,13,17,29,12)( 7,26,32,22,21, 9,25, 31,24,20, 8,27,33,23,19)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 2, 3)( 4,18,12,14,29, 6,17,11,13,28, 5,16,10,15,30)( 7,31,19,25,23, 9,33, 21,27,22, 8,32,20,26,24)$
$ 30, 3 $ $11$ $30$ $( 1, 2, 3)( 4,19,12,23,29,33,17,27,13, 8, 5,20,10,24,30,31,18,25,14, 9, 6,21, 11,22,28,32,16,26,15, 7)$
$ 30, 3 $ $11$ $30$ $( 1, 2, 3)( 4,24,16, 8,11,33,14,19,30,26, 5,22,17, 9,12,31,15,20,28,27, 6,23, 18, 7,10,32,13,21,29,25)$
$ 30, 3 $ $11$ $30$ $( 1, 2, 3)( 4,27,30,21,15,33,10, 9,16,23, 5,25,28,19,13,31,11, 7,17,24, 6,26, 29,20,14,32,12, 8,18,22)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 2, 3)( 4,29,13,10,18, 6,28,15,12,17, 5,30,14,11,16)( 7,23,27,20,31, 9,22, 26,19,33, 8,24,25,21,32)$
$ 6, 6, 6, 6, 6, 3 $ $11$ $6$ $( 1, 2, 3)( 4,32, 6,31, 5,33)( 7,28, 9,30, 8,29)(10,27,12,26,11,25) (13,23,15,22,14,24)(16,21,18,20,17,19)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20) (22,24,23)(25,27,26)(28,30,29)(31,33,32)$
$ 30, 3 $ $11$ $30$ $( 1, 3, 2)( 4, 7,15,26,16,32,28,22,11,21, 6, 9,14,25,18,31,30,24,10,20, 5, 8, 13,27,17,33,29,23,12,19)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 3, 2)( 4,12,29,17,13, 5,10,30,18,14, 6,11,28,16,15)( 7,19,23,33,27, 8,20, 24,31,25, 9,21,22,32,26)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 3, 2)( 4,13,18,28,12, 5,14,16,29,10, 6,15,17,30,11)( 7,27,31,22,19, 8,25, 32,23,20, 9,26,33,24,21)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 3, 2)( 4,16,11,14,30, 5,17,12,15,28, 6,18,10,13,29)( 7,32,21,25,24, 8,33, 19,26,22, 9,31,20,27,23)$
$ 30, 3 $ $11$ $30$ $( 1, 3, 2)( 4,20,11,23,30,32,17,25,15, 8, 6,19,10,22,29,31,16,27,14, 7, 5,21, 12,24,28,33,18,26,13, 9)$
$ 30, 3 $ $11$ $30$ $( 1, 3, 2)( 4,22,18, 8,12,32,14,20,29,26, 6,24,17, 7,11,31,13,19,28,25, 5,23, 16, 9,10,33,15,21,30,27)$
$ 30, 3 $ $11$ $30$ $( 1, 3, 2)( 4,25,29,21,13,32,10, 7,18,23, 6,27,28,20,15,31,12, 9,17,22, 5,26, 30,19,14,33,11, 8,16,24)$
$ 15, 15, 3 $ $11$ $15$ $( 1, 3, 2)( 4,30,15,10,16, 5,28,13,11,17, 6,29,14,12,18)( 7,24,26,20,32, 8,22, 27,21,33, 9,23,25,19,31)$
$ 6, 6, 6, 6, 6, 3 $ $11$ $6$ $( 1, 3, 2)( 4,33, 5,31, 6,32)( 7,29, 8,30, 9,28)(10,25,11,26,12,27) (13,24,14,22,15,23)(16,19,17,20,18,21)$
$ 11, 11, 11 $ $10$ $11$ $( 1, 4, 8,10,14,17,21,23,26,28,31)( 2, 5, 9,11,15,18,19,24,27,29,32) ( 3, 6, 7,12,13,16,20,22,25,30,33)$
$ 33 $ $10$ $33$ $( 1, 5, 7,10,15,16,21,24,25,28,32, 3, 4, 9,12,14,18,20,23,27,30,31, 2, 6, 8, 11,13,17,19,22,26,29,33)$
$ 33 $ $10$ $33$ $( 1, 6, 9,10,13,18,21,22,27,28,33, 2, 4, 7,11,14,16,19,23,25,29,31, 3, 5, 8, 12,15,17,20,24,26,30,32)$

Group invariants

Order:  $330=2 \cdot 3 \cdot 5 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [330, 1]
Character table: Data not available.