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Properties

Label 33T14
Degree $33$
Order $726$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}^2:S_3$

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Show commands: Magma

magma: G := TransitiveGroup(33, 14);
 

Group action invariants

Degree $n$:  $33$
magma: t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $14$
magma: t, n := TransitiveGroupIdentification(G); t;
 
Group:  $C_{11}^2:S_3$
Parity:  $1$
magma: IsEven(G);
 
Primitive:  no
magma: IsPrimitive(G);
 
magma: NilpotencyClass(G);
 
$\card{\Aut(F/K)}$:  $1$
magma: Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  (1,27,22)(2,32,15)(3,26,19)(4,31,12)(5,25,16)(6,30,20)(7,24,13)(8,29,17)(9,23,21)(10,28,14)(11,33,18), (1,19,10,16,8,13,6,21,4,18,2,15,11,12,9,20,7,17,5,14,3,22)(23,27)(24,26)(28,33)(29,32)(30,31)
magma: Generators(G);
 

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$6$:  $S_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T13

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

magma: ConjugacyClasses(G);
 

Group invariants

Order:  $726=2 \cdot 3 \cdot 11^{2}$
magma: Order(G);
 
Cyclic:  no
magma: IsCyclic(G);
 
Abelian:  no
magma: IsAbelian(G);
 
Solvable:  yes
magma: IsSolvable(G);
 
Nilpotency class:   not nilpotent
Label:  726.5
magma: IdentifyGroup(G);
 
Character table: not available.

magma: CharacterTable(G);