Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×#66526 |
| unambiguous semidirect product | C5⋊(C22×#66526) |
| unambiguous semidirect product | (C2×C5)⋊(C2×#66526) |
| Fitting, socle | C2×C5×C37 ⋊ C2×C9 |
| derived, Hall | C5×C37 ⋊ C22×C9 |
| Hall | C5×#66526 ⋊ C22 |
| Hall | C2×D5×C37 ⋊ C9 |
| Sylow | C37 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C22×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×#66526 |
| commutator, hypocenter | C5×C37 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C37 | C2×C9 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
104 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D25×#66526, D52×#66526, C2×C5×D5×#66526, … |
| maximal normal subgroup of | C2×C5×D5×#66526 |
| maximal quotient of | C2×D25×#66526, D52×#66526, C2×C5×D5×#66526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 87);