Show commands:
Magma
magma: G := TransitiveGroup(33, 41);
Group action invariants
Degree $n$: | $33$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $41$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_{11}^3:C_{30}$ | ||
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: | (1,18,25,6,19,23,4,12,26,7,17,27,8,15,31)(2,16,29,10,22,28,9,13,24,5,21,30,11,20,32)(3,14,33), (1,5,2,7,6,4,11,3,9,10)(12,17,16,14,21,13,19,20,22,15)(23,24,26,30,27,32,31,29,25,28) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $5$: $C_5$ $6$: $C_6$ $10$: $C_{10}$ $15$: $C_{15}$ $30$: $C_{30}$ $110$: $F_{11}$ $330$: 33T8 $3630$: 33T19 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 11: None
Low degree siblings
33T41 x 39Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 77 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.d | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);