Show commands:
Magma
magma: G := TransitiveGroup(33, 29);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $29$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_3^5:C_{33}$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $3$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,33,29,26,23,20,17,13,11,8,5,2,31,30,27,24,21,18,14,12,9,6,3,32,28,25,22,19,16,15,10,7,4), (1,22,11,31,20,9,28,16,6,25,15,2,23,12,32,21,7,29,17,4,26,13,3,24,10,33,19,8,30,18,5,27,14) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $11$: $C_{11}$ $33$: $C_{33}$ $2673$: 33T18 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 11: $C_{11}$
Low degree siblings
33T29 x 21Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 99 conjugacy class representatives for $C_3^5:C_{33}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $8019=3^{6} \cdot 11$ | 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: | 8019.505 | magma: IdentifyGroup(G);
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| Character table: | 99 x 99 character table |
magma: CharacterTable(G);