Finite Group DatabasebetaFinite Group Databasebeta| order | 9930 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C331⋊C5 |
| unambiguous semidirect product | (C2×C3×C331)⋊C5 |
| Fitting, socle, Hall | C2×C3×C331 ⋊ C5 |
| derived, Sylow | C331 ⋊ C2×C3×C5 |
| Hall | C3×C331 ⋊ C2×C5 |
| Hall | C2×C331 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C331⋊C5 |
| commutator, cosocle, hypocenter | C331 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C331 | C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
426 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C331⋊C5, C3×Dic331⋊C5, Dic3×C331⋊C5, … |
| maximal normal subgroup of | C3×C4×C331⋊C5, C3×Dic331⋊C5, Dic3×C331⋊C5, … |
| maximal quotient of | C3×C4×C331⋊C5, C22×C3×C331⋊C5, C2×C9×C331⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9930, 2);