Finite Group DatabasebetaFinite Group Databasebeta| order | 4530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C151⋊C5 |
| unambiguous semidirect product | (C2×C3×C151)⋊C5 |
| Fitting, socle, Hall | C2×C3×C151 ⋊ C5 |
| derived, Sylow | C151 ⋊ C2×C3×C5 |
| Hall | C3×C151 ⋊ C2×C5 |
| Hall | C2×C151 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C151⋊C5 |
| commutator, cosocle, hypocenter | C151 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C151 | C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 156 |
| transitive degree | μt(G) = 906 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4530, 2);