Finite Group DatabasebetaFinite Group Databasebeta| order | 4530 |
| automorphism | Aut(G) order 2718000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2265 |
| unambiguous semidirect product | C3⋊D755 |
| unambiguous semidirect product | C5⋊D453 |
| unambiguous semidirect product | C151⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C151 ⋊ C2 |
| Hall | C5×C151 ⋊ D3 |
| Hall | C3×C151 ⋊ D5 |
| Sylow | C151 ⋊ D15 |
| Hall | C3×C5 ⋊ D151 |
| Sylow | C5 ⋊ D453 |
| Sylow | C3 ⋊ D755 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C151 | C2 |
| LCS | G ▷ C3×C5×C151 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 159 |
| transitive degree | μt(G) = 2265 |
Polycyclic presentation:
2,3,5,151|b^a=b^2,c^a=c^4,d^a=d^1501134 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D6795, C3⋊(C5⋊(D151⋊C3)), C3⋊D2265, … |
| maximal normal subgroup of | C3⋊(C5⋊(D151⋊C3)), C3×D2265, C3⋊(C5⋊(D151⋊C5)), … |
| maximal quotient of | D6795, C3⋊D2265, C3×D2265, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4530, 11);