Show commands:
Magma
magma: G := TransitiveGroup(38, 39);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{19}^2:C_3:C_{36}$ | ||
| 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: | (1,7,12,13,17,14,2,11,9)(3,15,6,8,16,10,5,4,19)(20,35,37,36,27,22,34,28,31)(21,25,23,24,33,38,26,32,29), (1,24,7,20,2,36,3,29,18,38,15,21,8,32,17,26,19,31,11,30,5,34,10,37,9,25,13,35,16,33,4,22,14,28,12,23)(6,27) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $4$: $C_4$ $6$: $S_3$, $C_6$ $9$: $C_9$ $12$: $C_{12}$, $C_3 : C_4$ $18$: $S_3\times C_3$, $C_{18}$ $36$: $C_3\times (C_3 : C_4)$, $C_{36}$ $54$: $C_9\times S_3$ $108$: 36T62 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 60 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $38988=2^{2} \cdot 3^{3} \cdot 19^{2}$ | 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: | 38988.p | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);