Show commands:
Magma
magma: G := TransitiveGroup(38, 36);
Group action invariants
| Degree $n$: | $38$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $36$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $D_{19}^2:C_{18}$ | ||
| 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: | (1,2)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)(20,25,30,35,21,26,31,36,22,27,32,37,23,28,33,38,24,29,34), (1,21)(2,29,11,25,6,23,13,22,7,31,4,26,12,33,16,27,18,24,19,32,10,36,15,38,8,20,14,30,17,35,9,28,5,34,3,37) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ x 3 $3$: $C_3$ $4$: $C_2^2$ $6$: $C_6$ x 3 $8$: $D_{4}$ $9$: $C_9$ $12$: $C_6\times C_2$ $18$: $C_{18}$ x 3 $24$: $D_4 \times C_3$ $36$: 36T2 $72$: 36T15 Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 19: None
Low degree siblings
38T36Siblings are shown 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: | $25992=2^{3} \cdot 3^{2} \cdot 19^{2}$ | 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: | 25992.bj | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);