Show commands:
Magma
magma: G := TransitiveGroup(38, 10);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $10$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{19}\times D_{19}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $19$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,18,16,14,12,10,8,6,4,2,19,17,15,13,11,9,7,5,3)(20,23,26,29,32,35,38,22,25,28,31,34,37,21,24,27,30,33,36), (1,25,18,33,16,22,14,30,12,38,10,27,8,35,6,24,4,32,2,21,19,29,17,37,15,26,13,34,11,23,9,31,7,20,5,28,3,36) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $19$: $C_{19}$ $38$: $D_{19}$, $C_{38}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T10 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 209 conjugacy class representatives for $C_{19}\times D_{19}$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $722=2 \cdot 19^{2}$ | 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: | 722.3 | magma: IdentifyGroup(G);
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| Character table: | 209 x 209 character table |
magma: CharacterTable(G);