Finite Group DatabasebetaFinite Group Databasebeta| order | 3330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C37⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C5×C37⋊C3) |
| unambiguous semidirect product | (D3×C37)⋊(C3×C5) |
| unambiguous semidirect product | (C5×D3×C37)⋊C3 |
| Fitting, socle | C3×C5×C37 ⋊ C2×C3 |
| derived | C3×C37 ⋊ C2×C3×C5 |
| Hall | C3×C5×C37⋊C3 ⋊ C2 |
| Hall | C3×C37⋊C3 ⋊ C2×C5 |
| Hall | C5×C37 ⋊ C3×D3 |
| Sylow | C37 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×C37⋊C3 |
| commutator, cosocle, hypocenter | C3×C37 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C37 | C2×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 555 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3330, 22);