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Magma
magma: G := TransitiveGroup(33, 15);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $15$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}^2:D_6$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $1$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,22,26,7,20,23)(2,18,31,6,13,29)(3,14,25,5,17,24)(4,21,30)(8,16,28,11,15,32)(9,12,33,10,19,27), (1,6,11,5,10,4,9,3,8,2,7)(12,33,14,30,16,27,18,24,20,32,22,29,13,26,15,23,17,31,19,28,21,25) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $6$: $S_3$ $12$: $D_{6}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T15Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
| Label | Cycle Type | Size | Order | Representative |
| $ 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 $ | $12$ | $11$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,16,20,13,17,21,14,18,22,15,19) (23,27,31,24,28,32,25,29,33,26,30)$ | |
| $ 11, 11, 11 $ | $12$ | $11$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,20,17,14,22,19,16,13,21,18,15) (23,31,28,25,33,30,27,24,32,29,26)$ | |
| $ 11, 11, 11 $ | $12$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,17,22,16,21,15,20,14,19,13,18) (23,28,33,27,32,26,31,25,30,24,29)$ | |
| $ 11, 11, 11 $ | $12$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,22,21,20,19,18,17,16,15,14,13) (23,33,32,31,30,29,28,27,26,25,24)$ | |
| $ 11, 11, 11 $ | $12$ | $11$ | $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,21,19,17,15,13,22,20,18,16,14) (23,32,30,28,26,24,33,31,29,27,25)$ | |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $(12,20,17,14,22,19,16,13,21,18,15)(23,24,25,26,27,28,29,30,31,32,33)$ | |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,17,22,16,21,15,20,14,19,13,18) (23,32,30,28,26,24,33,31,29,27,25)$ | |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,14,16,18,20,22,13,15,17,19,21) (23,29,24,30,25,31,26,32,27,33,28)$ | |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,19,15,22,18,14,21,17,13,20,16)$ | |
| $ 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 $ | $6$ | $11$ | $( 1, 9, 6, 3,11, 8, 5, 2,10, 7, 4)(23,27,31,24,28,32,25,29,33,26,30)$ | |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $(12,17,22,16,21,15,20,14,19,13,18)(23,25,27,29,31,33,24,26,28,30,32)$ | |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,22,21,20,19,18,17,16,15,14,13) (23,30,26,33,29,25,32,28,24,31,27)$ | |
| $ 11, 11, 11 $ | $6$ | $11$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,16,20,13,17,21,14,18,22,15,19) (23,24,25,26,27,28,29,30,31,32,33)$ | |
| $ 11, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $6$ | $11$ | $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(23,31,28,25,33,30,27,24,32,29,26)$ | |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $242$ | $3$ | $( 1,26,20)( 2,31,13)( 3,25,17)( 4,30,21)( 5,24,14)( 6,29,18)( 7,23,22) ( 8,28,15)( 9,33,19)(10,27,12)(11,32,16)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ | $121$ | $2$ | $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)(23,29) (24,28)(25,27)(30,33)(31,32)$ | |
| $ 6, 6, 6, 6, 6, 3 $ | $242$ | $6$ | $( 1,26,20, 8,24,15)( 2,32,13, 7,29,22)( 3,27,17, 6,23,18)( 4,33,21, 5,28,14) ( 9,30,19,11,31,16)(10,25,12)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ | $33$ | $2$ | $(12,27)(13,31)(14,24)(15,28)(16,32)(17,25)(18,29)(19,33)(20,26)(21,30)(22,23)$ | |
| $ 22, 11 $ | $66$ | $22$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,31,17,29,22,27,16,25,21,23,15,32,20,30, 14,28,19,26,13,24,18,33)$ | |
| $ 22, 11 $ | $66$ | $22$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,24,22,31,21,27,20,23,19,30,18,26,17,33, 16,29,15,25,14,32,13,28)$ | |
| $ 22, 11 $ | $66$ | $22$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,32,21,24,19,27,17,30,15,33,13,25,22,28, 20,31,18,23,16,26,14,29)$ | |
| $ 22, 11 $ | $66$ | $22$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,26,19,32,15,27,22,33,18,28,14,23,21,29, 17,24,13,30,20,25,16,31)$ | |
| $ 22, 11 $ | $66$ | $22$ | $( 1, 3, 5, 7, 9,11, 2, 4, 6, 8,10)(12,25,15,26,18,27,21,28,13,29,16,30,19,31, 22,32,14,33,17,23,20,24)$ | |
| $ 22, 2, 2, 2, 2, 2, 1 $ | $66$ | $22$ | $( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(12,25,18,23,13,32,19,30,14,28,20,26,15,24, 21,33,16,31,22,29,17,27)$ | |
| $ 22, 2, 2, 2, 2, 2, 1 $ | $66$ | $22$ | $( 1, 8)( 2, 7)( 3, 6)( 4, 5)( 9,11)(12,29,21,26,19,23,17,31,15,28,13,25,22,33, 20,30,18,27,16,24,14,32)$ | |
| $ 22, 2, 2, 2, 2, 2, 1 $ | $66$ | $22$ | $( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)(12,33,13,29,14,25,15,32,16,28,17,24,18,31, 19,27,20,23,21,30,22,26)$ | |
| $ 22, 2, 2, 2, 2, 2, 1 $ | $66$ | $22$ | $( 1, 7)( 2, 6)( 3, 5)( 8,11)( 9,10)(12,30,19,24,15,29,22,23,18,28,14,33,21,27, 17,32,13,26,20,31,16,25)$ | |
| $ 22, 2, 2, 2, 2, 2, 1 $ | $66$ | $22$ | $( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24,20,25,17,26,14,27,22,28,19,29,16,30, 13,31,21,32,18,33,15,23)$ | |
| $ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1 $ | $33$ | $2$ | $( 1, 9)( 2, 8)( 3, 7)( 4, 6)(10,11)(12,28)(13,24)(14,31)(15,27)(16,23)(17,30) (18,26)(19,33)(20,29)(21,25)(22,32)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1452=2^{2} \cdot 3 \cdot 11^{2}$ | magma: Order(G);
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| Cyclic: | no | magma: IsCyclic(G);
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| Abelian: | no | magma: IsAbelian(G);
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| Solvable: | yes | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 1452.22 | magma: IdentifyGroup(G);
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| Character table: | 31 x 31 character table |
magma: CharacterTable(G);