↑

Properties

Label 33T13
33T13 1 9 1->9 19 1->19 2 10 2->10 12 2->12 3 11 3->11 16 3->16 4 4->1 20 4->20 5 5->2 13 5->13 6 6->3 17 6->17 7 7->4 21 7->21 8 8->5 14 8->14 9->6 18 9->18 10->7 22 10->22 11->8 15 11->15 12->4 31 12->31 13->7 24 13->24 14->10 28 14->28 15->2 32 15->32 16->5 25 16->25 17->8 29 17->29 18->11 33 18->33 19->3 26 19->26 20->6 30 20->30 21->9 23 21->23 22->1 27 22->27 23->22 23->24 24->14 24->25 25->17 25->26 26->20 26->27 27->12 27->28 28->15 28->29 29->18 29->30 30->21 30->31 31->13 31->32 32->16 32->33 33->19 33->23
Degree $33$
Order $726$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{11}^2:S_3$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(33, 13);
 

Group invariants

Abstract group:  $C_{11}^2:S_3$
Copy content magma:IdentifyGroup(G);
 
Order:  $726=2 \cdot 3 \cdot 11^{2}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

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

Low degree resolvents

$\card{(G/N)}$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

33T14

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

LabelCycle TypeSizeOrderIndexRepresentative
1A $1^{33}$ $1$ $1$ $0$ $()$
2A $2^{11},1^{11}$ $33$ $2$ $11$ $(12,26)(13,30)(14,23)(15,27)(16,31)(17,24)(18,28)(19,32)(20,25)(21,29)(22,33)$
3A $3^{11}$ $242$ $3$ $22$ $( 1,25,21)( 2,30,14)( 3,24,18)( 4,29,22)( 5,23,15)( 6,28,19)( 7,33,12)( 8,27,16)( 9,32,20)(10,26,13)(11,31,17)$
11A1 $11^{3}$ $3$ $11$ $30$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,14,16,18,20,22,13,15,17,19,21)(23,31,28,25,33,30,27,24,32,29,26)$
11A-1 $11^{3}$ $3$ $11$ $30$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,21,19,17,15,13,22,20,18,16,14)(23,26,29,32,24,27,30,33,25,28,31)$
11A2 $11^{3}$ $3$ $11$ $30$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,16,20,13,17,21,14,18,22,15,19)(23,28,33,27,32,26,31,25,30,24,29)$
11A-2 $11^{3}$ $3$ $11$ $30$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,19,15,22,18,14,21,17,13,20,16)(23,29,24,30,25,31,26,32,27,33,28)$
11A3 $11^{3}$ $3$ $11$ $30$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,18,13,19,14,20,15,21,16,22,17)(23,25,27,29,31,33,24,26,28,30,32)$
11A-3 $11^{3}$ $3$ $11$ $30$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,17,22,16,21,15,20,14,19,13,18)(23,32,30,28,26,24,33,31,29,27,25)$
11A4 $11^{3}$ $3$ $11$ $30$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,20,17,14,22,19,16,13,21,18,15)(23,33,32,31,30,29,28,27,26,25,24)$
11A-4 $11^{3}$ $3$ $11$ $30$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,15,18,21,13,16,19,22,14,17,20)(23,24,25,26,27,28,29,30,31,32,33)$
11A5 $11^{3}$ $3$ $11$ $30$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,22,21,20,19,18,17,16,15,14,13)(23,30,26,33,29,25,32,28,24,31,27)$
11A-5 $11^{3}$ $3$ $11$ $30$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,13,14,15,16,17,18,19,20,21,22)(23,27,31,24,28,32,25,29,33,26,30)$
11B1 $11^{2},1^{11}$ $6$ $11$ $20$ $(12,21,19,17,15,13,22,20,18,16,14)(23,31,28,25,33,30,27,24,32,29,26)$
11B2 $11^{2},1^{11}$ $6$ $11$ $20$ $(12,19,15,22,18,14,21,17,13,20,16)(23,28,33,27,32,26,31,25,30,24,29)$
11B3 $11^{2},1^{11}$ $6$ $11$ $20$ $(12,17,22,16,21,15,20,14,19,13,18)(23,25,27,29,31,33,24,26,28,30,32)$
11B4 $11^{2},1^{11}$ $6$ $11$ $20$ $(12,15,18,21,13,16,19,22,14,17,20)(23,33,32,31,30,29,28,27,26,25,24)$
11B5 $11^{2},1^{11}$ $6$ $11$ $20$ $(12,13,14,15,16,17,18,19,20,21,22)(23,30,26,33,29,25,32,28,24,31,27)$
11C1 $11^{3}$ $6$ $11$ $30$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,20,17,14,22,19,16,13,21,18,15)(23,27,31,24,28,32,25,29,33,26,30)$
11C-1 $11^{3}$ $6$ $11$ $30$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,15,18,21,13,16,19,22,14,17,20)(23,30,26,33,29,25,32,28,24,31,27)$
11C2 $11^{3}$ $6$ $11$ $30$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,17,22,16,21,15,20,14,19,13,18)(23,31,28,25,33,30,27,24,32,29,26)$
11C-2 $11^{3}$ $6$ $11$ $30$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,18,13,19,14,20,15,21,16,22,17)(23,26,29,32,24,27,30,33,25,28,31)$
11C3 $11^{3}$ $6$ $11$ $30$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,14,16,18,20,22,13,15,17,19,21)(23,24,25,26,27,28,29,30,31,32,33)$
11C-3 $11^{3}$ $6$ $11$ $30$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,21,19,17,15,13,22,20,18,16,14)(23,33,32,31,30,29,28,27,26,25,24)$
11C4 $11^{3}$ $6$ $11$ $30$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,22,21,20,19,18,17,16,15,14,13)(23,28,33,27,32,26,31,25,30,24,29)$
11C-4 $11^{3}$ $6$ $11$ $30$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,13,14,15,16,17,18,19,20,21,22)(23,29,24,30,25,31,26,32,27,33,28)$
11C5 $11^{3}$ $6$ $11$ $30$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,19,15,22,18,14,21,17,13,20,16)(23,32,30,28,26,24,33,31,29,27,25)$
11C-5 $11^{3}$ $6$ $11$ $30$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,16,20,13,17,21,14,18,22,15,19)(23,25,27,29,31,33,24,26,28,30,32)$
22A1 $22,11$ $33$ $22$ $31$ $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,30,14,27,16,24,18,32,20,29,22,26,13,23,15,31,17,28,19,25,21,33)$
22A-1 $22,11$ $33$ $22$ $31$ $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,33,21,25,19,28,17,31,15,23,13,26,22,29,20,32,18,24,16,27,14,30)$
22A3 $22,11$ $33$ $22$ $31$ $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,27,18,29,13,31,19,33,14,24,20,26,15,28,21,30,16,32,22,23,17,25)$
22A-3 $22,11$ $33$ $22$ $31$ $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,25,17,23,22,32,16,30,21,28,15,26,20,24,14,33,19,31,13,29,18,27)$
22A5 $22,11$ $33$ $22$ $31$ $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,24,22,31,21,27,20,23,19,30,18,26,17,33,16,29,15,25,14,32,13,28)$
22A-5 $22,11$ $33$ $22$ $31$ $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(12,28,13,32,14,25,15,29,16,33,17,26,18,30,19,23,20,27,21,31,22,24)$
22A7 $22,11$ $33$ $22$ $31$ $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,32,15,33,18,23,21,24,13,25,16,26,19,27,22,28,14,29,17,30,20,31)$
22A-7 $22,11$ $33$ $22$ $31$ $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,31,20,30,17,29,14,28,22,27,19,26,16,25,13,24,21,23,18,33,15,32)$
22A9 $22,11$ $33$ $22$ $31$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,29,19,24,15,30,22,25,18,31,14,26,21,32,17,27,13,33,20,28,16,23)$
22A-9 $22,11$ $33$ $22$ $31$ $( 1,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(12,23,16,28,20,33,13,27,17,32,21,26,14,31,18,25,22,30,15,24,19,29)$

Malle's constant $a(G)$:     $1/11$

Copy content magma:ConjugacyClasses(G);
 

Character table

38 x 38 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed