Show commands:
Magma
magma: G := TransitiveGroup(38, 16);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $16$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{19}^2:D_6$ | ||
| 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: | (1,9,16,15,7,19)(2,17,4,14,18,12)(3,6,11,13,10,5)(20,31,30,37,26,27)(21,24,22,36,33,35)(23,29,25,34,28,32), (1,27,12,33,4,20,15,26,7,32,18,38,10,25,2,31,13,37,5,24,16,30,8,36,19,23,11,29,3,35,14,22,6,28,17,34,9,21) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $6$: $S_3$ $12$: $D_{6}$ 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 63 conjugacy class representatives for $C_{19}^2:D_6$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $4332=2^{2} \cdot 3 \cdot 19^{2}$ | 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: | 4332.n | magma: IdentifyGroup(G);
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| Character table: | 63 x 63 character table |
magma: CharacterTable(G);