Show commands:
Magma
magma: G := TransitiveGroup(38, 13);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $13$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| 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: | (1,24,16,26,12,28,8,30,4,32,19,34,15,36,11,38,7,21,3,23,18,25,14,27,10,29,6,31,2,33,17,35,13,37,9,20,5,22), (1,9,2)(3,12,16)(5,15,11)(6,7,18)(8,10,13)(14,19,17)(20,21,28)(22,35,31)(24,30,34)(25,37,26)(27,32,29)(33,36,38) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
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
The 90 conjugacy class representatives for t38n13
magma: ConjugacyClasses(G);
Group invariants
| Order: | $2166=2 \cdot 3 \cdot 19^{2}$ | 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: | 2166.11 | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);