Finite Group DatabasebetaFinite Group Databasebeta| order | 4530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×D151⋊C5 |
| unambiguous semidirect product | (C3×D151)⋊C5 |
| Fitting, socle, Hall | C3×C151 ⋊ C2×C5 |
| derived, Sylow | C151 ⋊ C2×C3×C5 |
| Hall | C3×C151⋊C5 ⋊ C2 |
| Hall | C3×D151 ⋊ C5 |
| Hall | C151⋊C5 ⋊ C2×C3 |
| Hall | D151 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D151⋊C5 |
| commutator, cosocle, hypocenter | C151 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C151 | C2×C5 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 154 |
| transitive degree | μt(G) = 453 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D151⋊C5, (D151⋊C5)⋊C9, C3×(D151⋊C3)⋊C5, … |
| maximal normal subgroup of | C9×D151⋊C5, (D151⋊C5)⋊C9, C3×(D151⋊C3)⋊C5, … |
| maximal quotient of | C9×D151⋊C5, C32×D151⋊C5, C3×C3⋊(D151⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4530, 12);