Show commands:
Magma
magma: G := TransitiveGroup(38, 11);
Group action invariants
Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $11$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $D_{19}^2$ | ||
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: | (1,27,10,25,19,23,9,21,18,38,8,36,17,34,7,32,16,30,6,28,15,26,5,24,14,22,4,20,13,37,3,35,12,33,2,31,11,29), (1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $38$: $D_{19}$ x 2 $76$: $D_{38}$ x 2 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T11 x 8Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 121 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $1444=2^{2} \cdot 19^{2}$ | 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: | 1444.9 | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);