Show commands:
Magma
magma: G := TransitiveGroup(15, 25);
Group action invariants
| Degree $n$: | $15$ | 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: | $C_5\wr C_3$ | ||
| CHM label: | $[5^{3}]3=5wr3$ | ||
| 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: | (1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15), (3,6,9,12,15) | magma: Generators(G);
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Low degree resolvents
|G/N| Galois groups for stem field(s) $3$: $C_3$ $5$: $C_5$ $15$: $C_{15}$ $75$: $C_5^2 : C_3$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 3: $C_3$
Degree 5: None
Low degree siblings
15T25 x 7Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
The 55 conjugacy class representatives for $C_5\wr C_3$
magma: ConjugacyClasses(G);
Group invariants
| Order: | $375=3 \cdot 5^{3}$ | 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: | 375.6 | magma: IdentifyGroup(G);
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| Character table: | 55 x 55 character table |
magma: CharacterTable(G);