Show commands:
Magma
magma: G := TransitiveGroup(38, 50);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $50$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_2^{18}.D_{19}$ | ||
| Parity: | $1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $2$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,30,2,29)(3,28,4,27)(5,25,6,26)(7,23)(8,24)(9,21,10,22)(11,20)(12,19)(13,18,14,17)(15,16)(31,38)(32,37)(33,35)(34,36), (1,37,2,38)(3,36)(4,35)(5,33)(6,34)(7,32,8,31)(9,29,10,30)(11,28,12,27)(13,26)(14,25)(15,23,16,24)(17,21,18,22) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $38$: $D_{19}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 19: $D_{19}$
Low degree siblings
38T50 x 510, 38T51 x 511Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 7676 conjugacy class representatives for $C_2^{18}.D_{19}$ 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.b | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);