Show commands:
Magma
magma: G := TransitiveGroup(38, 20);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $20$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{19}^2:D_9$ | ||
| 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: | (1,18,19,9,14,2,8,5,16)(3,17,10,4,7,15,11,13,12)(20,25,34,35,33,37,29,26,32)(21,23,38,27,30,24,36,31,22), (1,25,5,32,9,20,13,27,17,34,2,22,6,29,10,36,14,24,18,31,3,38,7,26,11,33,15,21,19,28,4,35,8,23,12,30,16,37) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $6$: $S_3$ $18$: $D_{9}$ 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
There are 53 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $6498=2 \cdot 3^{2} \cdot 19^{2}$ | 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: | 6498.m | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);