Show commands:
Magma
magma: G := TransitiveGroup(21, 145);
Group action invariants
| Degree $n$: | $21$ | magma: t, n := TransitiveGroupIdentification(G); n;
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| Transitive number $t$: | $145$ | magma: t, n := TransitiveGroupIdentification(G); t;
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| Group: | $C_3^7.C_2^6:\GL(3,2)$ | ||
| 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: | (1,7,3,9)(2,8)(4,11,17,13,6,10,16,15)(5,12,18,14)(19,20,21), (1,10,18,5,9,19,14,3,11,17,6,8,20,15,2,12,16,4,7,21,13) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $168$: $\GL(3,2)$ $1344$: $C_2^3:\GL(3,2)$ $10752$: 14T50 Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: None
Degree 7: $\GL(3,2)$
Low degree siblings
42T2982, 42T2983, 42T2984, 42T2986Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 132 conjugacy class representatives for $C_3^7.C_2^6:\GL(3,2)$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $23514624=2^{9} \cdot 3^{8} \cdot 7$ | 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: | 23514624.a | magma: IdentifyGroup(G);
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| Character table: | 132 x 132 character table |
magma: CharacterTable(G);