Finite Group DatabasebetaFinite Group Databasebeta| order | 3330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#66526⋊C2 |
| unambiguous semidirect product | #66526⋊(C2×C5) |
| Fitting, socle, Hall | C5×C37 ⋊ C2×C9 |
| derived, Sylow | C37 ⋊ C2×C5×C9 |
| Hall | C5×#66526 ⋊ C2 |
| Hall | C5×D37 ⋊ C9 |
| Hall | #66526 ⋊ C2×C5 |
| Hall | D37 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #66526⋊C2 |
| commutator, hypocenter | C37 | C2×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37 | C2×C9 |
| prime radical | C5×D37⋊C3 | C3 |
| cosocle | C37⋊C3 | C2×C3×C5 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 185 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3330, 14);