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Magma
magma: G := TransitiveGroup(33, 1);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $1$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{33}$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $33$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,30,23,17,11,6,31,26,20,13,8,2,28,24,18,12,4,32,27,21,14,9,3,29,22,16,10,5,33,25,19,15,7) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $11$: $C_{11}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: $C_{11}$
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
| 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 $ | $1$ | $1$ | $()$ | |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $1$ | $3$ | $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)(28,29,30)(31,32,33)$ | |
| $ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ | $1$ | $3$ | $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20) (22,24,23)(25,27,26)(28,30,29)(31,33,32)$ | |
| $ 33 $ | $1$ | $33$ | $( 1, 4, 7,12,15,18,19,24,25,28,33, 2, 5, 8,10,13,16,20,22,26,29,31, 3, 6, 9, 11,14,17,21,23,27,30,32)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1, 5, 9,12,13,17,19,22,27,28,31)( 2, 6, 7,10,14,18,20,23,25,29,32) ( 3, 4, 8,11,15,16,21,24,26,30,33)$ | |
| $ 33 $ | $1$ | $33$ | $( 1, 6, 8,12,14,16,19,23,26,28,32, 3, 5, 7,11,13,18,21,22,25,30,31, 2, 4, 9, 10,15,17,20,24,27,29,33)$ | |
| $ 33 $ | $1$ | $33$ | $( 1, 7,15,19,25,33, 5,10,16,22,29, 3, 9,14,21,27,32, 4,12,18,24,28, 2, 8,13, 20,26,31, 6,11,17,23,30)$ | |
| $ 33 $ | $1$ | $33$ | $( 1, 8,14,19,26,32, 5,11,18,22,30, 2, 9,15,20,27,33, 6,12,16,23,28, 3, 7,13, 21,25,31, 4,10,17,24,29)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1, 9,13,19,27,31, 5,12,17,22,28)( 2, 7,14,20,25,32, 6,10,18,23,29) ( 3, 8,15,21,26,33, 4,11,16,24,30)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,10,21,28, 6,15,22,32, 8,17,25, 3,12,20,30, 5,14,24,31, 7,16,27, 2,11,19, 29, 4,13,23,33, 9,18,26)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,11,20,28, 4,14,22,33, 7,17,26, 2,12,21,29, 5,15,23,31, 8,18,27, 3,10,19, 30, 6,13,24,32, 9,16,25)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,12,19,28, 5,13,22,31, 9,17,27)( 2,10,20,29, 6,14,23,32, 7,18,25) ( 3,11,21,30, 4,15,24,33, 8,16,26)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,13,27, 5,17,28, 9,19,31,12,22)( 2,14,25, 6,18,29, 7,20,32,10,23) ( 3,15,26, 4,16,30, 8,21,33,11,24)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,14,26, 5,18,30, 9,20,33,12,23, 3,13,25, 4,17,29, 8,19,32,11,22, 2,15,27, 6,16,28, 7,21,31,10,24)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,15,25, 5,16,29, 9,21,32,12,24, 2,13,26, 6,17,30, 7,19,33,10,22, 3,14,27, 4,18,28, 8,20,31,11,23)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,16,32,13,30,10,27, 8,23, 5,21, 2,17,33,14,28,11,25, 9,24, 6,19, 3,18,31, 15,29,12,26, 7,22, 4,20)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,17,31,13,28,12,27, 9,22, 5,19)( 2,18,32,14,29,10,25, 7,23, 6,20) ( 3,16,33,15,30,11,26, 8,24, 4,21)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,18,33,13,29,11,27, 7,24, 5,20, 3,17,32,15,28,10,26, 9,23, 4,19, 2,16,31, 14,30,12,25, 8,22, 6,21)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,19, 5,22, 9,27,12,28,13,31,17)( 2,20, 6,23, 7,25,10,29,14,32,18) ( 3,21, 4,24, 8,26,11,30,15,33,16)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,20, 4,22, 7,26,12,29,15,31,18, 3,19, 6,24, 9,25,11,28,14,33,17, 2,21, 5, 23, 8,27,10,30,13,32,16)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,21, 6,22, 8,25,12,30,14,31,16, 2,19, 4,23, 9,26,10,28,15,32,17, 3,20, 5, 24, 7,27,11,29,13,33,18)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,22,12,31,19, 9,28,17, 5,27,13)( 2,23,10,32,20, 7,29,18, 6,25,14) ( 3,24,11,33,21, 8,30,16, 4,26,15)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,23,11,31,20, 8,28,18, 4,27,14, 3,22,10,33,19, 7,30,17, 6,26,13, 2,24,12, 32,21, 9,29,16, 5,25,15)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,24,10,31,21, 7,28,16, 6,27,15, 2,22,11,32,19, 8,29,17, 4,25,13, 3,23,12, 33,20, 9,30,18, 5,26,14)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,25,16, 9,32,24,13, 6,30,19,10, 3,27,18, 8,31,23,15, 5,29,21,12, 2,26,17, 7,33,22,14, 4,28,20,11)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,26,18, 9,33,23,13, 4,29,19,11, 2,27,16, 7,31,24,14, 5,30,20,12, 3,25,17, 8,32,22,15, 6,28,21,10)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,27,17, 9,31,22,13, 5,28,19,12)( 2,25,18, 7,32,23,14, 6,29,20,10) ( 3,26,16, 8,33,24,15, 4,30,21,11)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,28,22,17,12, 5,31,27,19,13, 9)( 2,29,23,18,10, 6,32,25,20,14, 7) ( 3,30,24,16,11, 4,33,26,21,15, 8)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,29,24,17,10, 4,31,25,21,13, 7, 3,28,23,16,12, 6,33,27,20,15, 9, 2,30,22, 18,11, 5,32,26,19,14, 8)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,30,23,17,11, 6,31,26,20,13, 8, 2,28,24,18,12, 4,32,27,21,14, 9, 3,29,22, 16,10, 5,33,25,19,15, 7)$ | |
| $ 11, 11, 11 $ | $1$ | $11$ | $( 1,31,28,27,22,19,17,13,12, 9, 5)( 2,32,29,25,23,20,18,14,10, 7, 6) ( 3,33,30,26,24,21,16,15,11, 8, 4)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,32,30,27,23,21,17,14,11, 9, 6, 3,31,29,26,22,20,16,13,10, 8, 5, 2,33,28, 25,24,19,18,15,12, 7, 4)$ | |
| $ 33 $ | $1$ | $33$ | $( 1,33,29,27,24,20,17,15,10, 9, 4, 2,31,30,25,22,21,18,13,11, 7, 5, 3,32,28, 26,23,19,16,14,12, 8, 6)$ |
magma: ConjugacyClasses(G);
Group invariants
| Order: | $33=3 \cdot 11$ | magma: Order(G);
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| Cyclic: | yes | magma: IsCyclic(G);
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| Abelian: | yes | magma: IsAbelian(G);
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| Solvable: | yes | magma: IsSolvable(G);
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| Nilpotency class: | $1$ | ||
| Label: | 33.1 | magma: IdentifyGroup(G);
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| Character table: | 33 x 33 character table |
magma: CharacterTable(G);