Show commands:
Magma
magma: G := TransitiveGroup(33, 42);
Group action invariants
| Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $42$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{11}^3:(C_5\times S_3)$ | ||
| 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: | (1,29,16,11,28,22,8,25,18,10,27,17,5,33,14)(2,30,21,3,31,15,6,23,19,4,32,20,9,26,12)(7,24,13), (1,30,9,27,8,26,4,33,10,28)(2,31)(3,32,6,24,7,25,11,29,5,23)(12,22,13,20,17)(14,18,21,15,16) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $6$: $S_3$ $10$: $C_{10}$ $30$: $S_3 \times C_5$ $55$: $C_{11}:C_5$ $110$: 22T5 $330$: 33T7 $3630$: 33T20 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $S_3$
Degree 11: None
Low degree siblings
33T42 x 9Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 98 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $39930=2 \cdot 3 \cdot 5 \cdot 11^{3}$ | 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: | 39930.f | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);