Show commands:
Magma
magma: G := TransitiveGroup(35, 41);
Group action invariants
| Degree $n$: | $35$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $41$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_5\times S_7$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | no | magma: IsPrimitive(G);
| magma: NilpotencyClass(G);
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| $\card{\Aut(F/K)}$: | $5$ | magma: Order(Centralizer(SymmetricGroup(n), G));
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| Generators: | (1,21,6,26,16)(2,22,7,27,17)(3,23,8,28,18)(4,24,9,29,19)(5,25,10,30,20)(11,31)(12,32)(13,33)(14,34)(15,35), (1,14,22,20,8,31,29,2,15,23,16,9,32,30,3,11,24,17,10,33,26,4,12,25,18,6,34,27,5,13,21,19,7,35,28) | magma: Generators(G);
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ $5$: $C_5$ $10$: $C_{10}$ $5040$: $S_7$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 5: $C_5$
Degree 7: $S_7$
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
Conjugacy classes not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $25200=2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7$ | 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: | no | magma: IsSolvable(G);
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| Nilpotency class: | not nilpotent | ||
| Label: | 25200.l | magma: IdentifyGroup(G);
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| Character table: | 75 x 75 character table |
magma: CharacterTable(G);