Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D111 |
| unambiguous semidirect product | (C3×D3)⋊(C5×D37) |
| unambiguous semidirect product | (D3×C37)⋊(C5×D3) |
| Fitting, socle, Hall | C32×C5×C37 ⋊ C22 |
| derived, Hall | C32×C37 ⋊ C22×C5 |
| Hall | C5×C37 ⋊ D32 |
| Hall | C32×C5 ⋊ C2×D37 |
| Sylow | C37 ⋊ C5×D32 |
| Sylow | C32 ⋊ C2×C5×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D111 |
| commutator, hypocenter | C32×C37 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C37 | C22 |
| LCS | G ▷ C32×C37 | |
| UCS | C1 ◁ C5 | |
88 conjugacy classes of subgroups.
855 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C25×D111, C52×D3×D111, C5×D3×D555, … |
| maximal normal subgroup of | D3×C25×D111, C52×D3×D111 |
| maximal quotient of | D3×C25×D111, C52×D3×D111, C5×D3×D555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 149);