Properties

Label 33T47
Order \(79860\)
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 $t$ :  $47$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,29,16,6,25,22,4,31,13,7,33,21,8,30,20)(2,26,15,10,24,18,9,27,19,5,28,12,11,32,17)(3,23,14), (1,33,18,11,27,14,10,32,21,9,26,17,8,31,13,7,25,20,6,30,16,5,24,12,4,29,19,3,23,15,2,28,22)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
5:  $C_5$
12:  $A_4$
15:  $C_{15}$
60:  20T14

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

44T296

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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $60$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,14,16,18,20,22,13,15,17,19,21)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $60$ $11$ $(12,21,19,17,15,13,22,20,18,16,14)(23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,14,16,18,20,22,13,15,17,19,21) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,18,13,19,14,20,15,21,16,22,17) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,15,18,21,13,16,19,22,14,17,20) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,20,17,14,22,19,16,13,21,18,15) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,19,15,22,18,14,21,17,13,20,16) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,17,22,16,21,15,20,14,19,13,18) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,13,14,15,16,17,18,19,20,21,22) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,22,21,20,19,18,17,16,15,14,13) (23,25,27,29,31,33,24,26,28,30,32)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,17,22,16,21,15,20,14,19,13,18) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,15,18,21,13,16,19,22,14,17,20) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 11 $ $60$ $11$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,22,21,20,19,18,17,16,15,14,13) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 11 $ $60$ $11$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,14,16,18,20,22,13,15,17,19,21) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,20,17,14,22,19,16,13,21,18,15) (23,27,31,24,28,32,25,29,33,26,30)$
$ 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $30$ $11$ $(23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,16,20,13,17,21,14,18,22,15,19) (23,24,25,26,27,28,29,30,31,32,33)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $60$ $11$ $(12,21,19,17,15,13,22,20,18,16,14)(23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $60$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 11 $ $20$ $11$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,14,16,18,20,22,13,15,17,19,21) (23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 11 $ $60$ $11$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,22,21,20,19,18,17,16,15,14,13) (23,26,29,32,24,27,30,33,25,28,31)$
$ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $60$ $11$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,20,17,14,22,19,16,13,21,18,15)$
$ 11, 11, 11 $ $20$ $11$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,22,21,20,19,18,17,16,15,14,13) (23,27,31,24,28,32,25,29,33,26,30)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $1331$ $5$ $( 2, 5, 6,10, 4)( 3, 9,11, 8, 7)(13,16,17,21,15)(14,20,22,19,18) (24,27,28,32,26)(25,31,33,30,29)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $1331$ $5$ $( 2, 6, 4, 5,10)( 3,11, 7, 9, 8)(13,17,15,16,21)(14,22,18,20,19) (24,28,26,27,32)(25,33,29,31,30)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $1331$ $5$ $( 2, 4,10, 6, 5)( 3, 7, 8,11, 9)(13,15,21,17,16)(14,18,19,22,20) (24,26,32,28,27)(25,29,30,33,31)$
$ 5, 5, 5, 5, 5, 5, 1, 1, 1 $ $1331$ $5$ $( 2,10, 5, 4, 6)( 3, 8, 9, 7,11)(13,21,16,15,17)(14,19,20,18,22) (24,32,27,26,28)(25,30,31,29,33)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $363$ $2$ $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(24,33)(25,32)(26,31)(27,30)(28,29)$
$ 11, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1 $ $3630$ $22$ $( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)(12,14,16,18,20,22,13,15,17,19,21)(24,33) (25,32)(26,31)(27,30)(28,29)$
$ 10, 10, 5, 5, 1, 1, 1 $ $3993$ $10$ $( 2, 8, 6, 3, 4,11, 5, 7,10, 9)(13,16,17,21,15)(14,20,22,19,18) (24,30,28,25,26,33,27,29,32,31)$
$ 10, 10, 5, 5, 1, 1, 1 $ $3993$ $10$ $( 2, 7, 4, 8,10,11, 6, 9, 5, 3)(13,17,15,16,21)(14,22,18,20,19) (24,29,26,30,32,33,28,31,27,25)$
$ 10, 10, 5, 5, 1, 1, 1 $ $3993$ $10$ $( 2, 9,10, 7, 5,11, 4, 3, 6, 8)(13,15,21,17,16)(14,18,19,22,20) (24,31,32,29,27,33,26,25,28,30)$
$ 10, 10, 5, 5, 1, 1, 1 $ $3993$ $10$ $( 2, 3, 5, 9, 6,11,10, 8, 4, 7)(13,21,16,15,17)(14,19,20,18,22) (24,25,27,31,28,33,32,30,26,29)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,29,16, 6,25,22, 4,31,13, 7,33,21, 8,30,20)( 2,26,15,10,24,18, 9,27,19, 5, 28,12,11,32,17)( 3,23,14)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,25,19, 6,31,16,10,27,18,11,26,13, 3,23,20)( 2,24,14, 9,28,12, 8,29,17, 5, 32,21, 7,30,22)( 4,33,15)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,31,17, 6,33,13, 9,32,15, 2,27,14,11,24,20)( 3,23,22, 5,26,16, 4,30,19,10, 28,12, 7,29,21)( 8,25,18)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,30,14, 7,31,15, 6,29,13, 8,33,17, 4,25,20)( 2,32,16, 5,27,22,10,26,21,11, 28,12, 9,24,19)( 3,23,18)$
$ 33 $ $2420$ $33$ $( 1,33,16, 2,28,12, 3,23,19, 4,29,15, 5,24,22, 6,30,18, 7,25,14, 8,31,21, 9, 26,17,10,32,13,11,27,20)$
$ 33 $ $2420$ $33$ $( 1,33,20, 7,25,18, 2,28,16, 8,31,14, 3,23,12, 9,26,21, 4,29,19,10,32,17, 5, 24,15,11,27,13, 6,30,22)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $484$ $3$ $( 1,33,13)( 2,28,20)( 3,23,16)( 4,29,12)( 5,24,19)( 6,30,15)( 7,25,22) ( 8,31,18)( 9,26,14)(10,32,21)(11,27,17)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,16,25, 4,13,33, 8,20,29, 6,22,31, 7,21,30)( 2,15,24, 9,19,28,11,17,26,10, 18,27, 5,12,32)( 3,14,23)$
$ 33 $ $2420$ $33$ $( 1,17,24,11,21,29,10,14,23, 9,18,28, 8,22,33, 7,15,27, 6,19,32, 5,12,26, 4, 16,31, 3,20,25, 2,13,30)$
$ 33 $ $2420$ $33$ $( 1,21,29, 5,16,31, 9,22,33, 2,17,24, 6,12,26,10,18,28, 3,13,30, 7,19,32,11, 14,23, 4,20,25, 8,15,27)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $484$ $3$ $( 1,20,25)( 2,16,31)( 3,12,26)( 4,19,32)( 5,15,27)( 6,22,33)( 7,18,28) ( 8,14,23)( 9,21,29)(10,17,24)(11,13,30)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,21,25, 5,12,24, 8,19,26, 2,16,33, 3,22,30)( 4,17,27,10,20,31, 9,14,23,11, 15,28, 7,13,29)( 6,18,32)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,13,31, 8,14,23, 7,17,32, 4,15,26, 6,20,30)( 2,21,33,11,16,29, 5,12,28, 9, 22,25,10,19,27)( 3,18,24)$
$ 15, 15, 3 $ $5324$ $15$ $( 1,15,32,10,22,29, 2,17,28, 3,19,24, 7,16,30)( 4,21,31,11,13,25, 6,14,23, 8, 18,26, 5,12,27)( 9,20,33)$

Group invariants

Order:  $79860=2^{2} \cdot 3 \cdot 5 \cdot 11^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.