Finite Group DatabasebetaFinite Group Databasebeta| order | 24630 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D821⋊C5) |
| unambiguous semidirect product | (C821⋊C5)⋊D3 |
| unambiguous semidirect product | D2463⋊C5 |
| Fitting, socle, derived, Hall | C3×C821 ⋊ C2×C5 |
| Hall | C3×C821⋊C5 ⋊ C2 |
| Hall | D2463 ⋊ C5 |
| Hall | C821⋊C5 ⋊ D3 |
| Sylow | C821 ⋊ C5×D3 |
| Sylow | C3 ⋊ D821⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C821 | C2×C5 |
| LCS | G ▷ C3×C821 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2463 |
Polycyclic presentation:
2,3,5,821|b^a=b^2,d^a=d^820,d^c=d^470261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24630, 12);