Show commands:
Magma
magma: G := TransitiveGroup(39, 25);
Group action invariants
| Degree $n$: | $39$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $25$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_{13}^2:C_6$ | ||
| 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: | (1,8)(2,7)(3,6)(4,5)(9,13)(10,12)(14,15)(16,26)(17,25)(18,24)(19,23)(20,22)(27,37)(28,36)(29,35)(30,34)(31,33)(38,39), (1,28,23,4,29,20)(2,37,22,3,33,21)(5,38,19,13,32,24)(6,34,18,12,36,25)(7,30,17,11,27,26)(8,39,16,10,31,14)(9,35,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $3$: $C_3$ $6$: $C_6$ $26$: $D_{13}$ $78$: $C_{13}:C_6$, 39T5 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 13: None
Low degree siblings
39T25 x 3Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 50 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1014=2 \cdot 3 \cdot 13^{2}$ | 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: | 1014.13 | magma: IdentifyGroup(G);
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| Character table: not available. |
magma: CharacterTable(G);