Finite Group DatabasebetaFinite Group Databasebeta| order | 15030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D835 |
| unambiguous semidirect product | C5⋊(C9×D167) |
| unambiguous semidirect product | C167⋊(C9×D5) |
| Fitting, Hall | C5×C9×C167 ⋊ C2 |
| derived, Hall | C5×C167 ⋊ C2×C9 |
| Hall | C9×C167 ⋊ D5 |
| Sylow | C167 ⋊ C9×D5 |
| Hall | C5×C9 ⋊ D167 |
| Sylow | C5 ⋊ C9×D167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D835 |
| commutator, hypocenter | C5×C167 | C2×C9 |
| Frattini | C3 | C3×D835 |
| Fitting | C5×C9×C167 | C2 |
| socle, cosocle | C3×C5×C167 | C2×C3 |
| prime radical | C3×D835 | C3 |
| LCS | G ▷ C5×C167 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7515 |
3771 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D167, D9×D835, D45⋊D167, … |
| maximal normal subgroup of | C9×D5×D167, D9×D835, D45⋊D167, … |
| maximal quotient of | C9×Dic835, C2×C9×D835 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15030, 4);