Show commands:
Magma
magma: G := TransitiveGroup(38, 49);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $49$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{18}.C_{38}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,32,24,16,8,38,29,22,14,6,35,28,20,12,3,34,26,17,10,2,31,23,15,7,37,30,21,13,5,36,27,19,11,4,33,25,18,9), (1,17,34,11,28,5,22,37,15,31,10,25,3,19,36,14,30,8,23,2,18,33,12,27,6,21,38,16,32,9,26,4,20,35,13,29,7,24) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $19$: $C_{19}$ $38$: $C_{38}$ $4980736$: 38T48 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 19: $C_{19}$
Low degree siblings
38T49 x 13796Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 27632 conjugacy class representatives for $C_2^{18}.C_{38}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $9961472=2^{19} \cdot 19$ | 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: | 9961472.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);