Finite Group DatabasebetaFinite Group Databasebeta| order | 24630 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C821⋊C5 |
| unambiguous semidirect product | (C2×C821)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C3×C821)⋊C5 |
| Fitting, socle, Hall | C2×C3×C821 ⋊ C5 |
| derived, Sylow | C821 ⋊ C2×C3×C5 |
| Hall | C3×C821 ⋊ C2×C5 |
| Hall | C2×C821 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C821⋊C5 |
| commutator, cosocle, hypocenter | C821 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C821 | C5 |
| LCS | G ▷ C821 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4926 |
1014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24630, 2);