Show commands:
Magma
magma: G := TransitiveGroup(42, 9491);
Group action invariants
| Degree $n$: | $42$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $9491$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $S_{42}$ | ||
| Parity: | $-1$ | magma: IsEven(G);
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| Primitive: | yes | 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: | (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42), (1,2) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $2$: $C_2$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: None
Degree 3: None
Degree 6: None
Degree 7: None
Degree 14: None
Degree 21: 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
The 53174 conjugacy class representatives for $S_{42}$ are not computed
magma: ConjugacyClasses(G);
Group invariants
| Order: | $1405006117752879898543142606244511569936384000000000=2^{39} \cdot 3^{19} \cdot 5^{9} \cdot 7^{6} \cdot 11^{3} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41$ | 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: | 1405006117752879898543142606244511569936384000000000.a | magma: IdentifyGroup(G);
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| Character table: | not computed |
magma: CharacterTable(G);