Show commands:
Magma
magma: G := TransitiveGroup(35, 46);
Group action invariants
Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
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Transitive number $t$: | $46$ | magma: t, n := TransitiveGroupIdentification(G); t;
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Group: | $C_7^4:F_5$ | ||
Parity: | $-1$ | magma: IsEven(G);
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Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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$\card{\Aut(F/K)}$: | $7$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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Generators: | (1,34,12,16)(2,30,11,18)(3,33,14,17)(4,29,9,15)(5,32,8,21)(6,35,13,19)(7,31,10,20), (1,21,26,13,4,20,23,11,6,17,27,8,2,16,25,10,5,15,22,14,7,19,24,12,3,18,28,9)(29,34,33,31,32,30,35) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ $4$: $C_4$ $20$: $F_5$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $F_5$
Degree 7: None
Low degree siblings
35T47Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
There are 179 conjugacy classes of elements. Data not shown.
magma: ConjugacyClasses(G);
Group invariants
Order: | $48020=2^{2} \cdot 5 \cdot 7^{4}$ | 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: | 48020.g | magma: IdentifyGroup(G);
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Character table: not available. |
magma: CharacterTable(G);