Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| isoclinism | isoclinic class of #66526 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×C5×#66526 |
| Fitting, Hall | C4×C5×C37 ⋊ C9 |
| derived, Sylow | C37 ⋊ C4×C5×C9 |
| Hall | C5×C37 ⋊ C4×C9 |
| Hall | C4×C37 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | #66526 |
| commutator, hypocenter | C37 | C4×C5×C9 |
| Frattini | C2 | C2×C5×#66526 |
| Fitting | C4×C5×C37 | C9 |
| socle | C2×C5×C37 | C2×C9 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C4×C5 | |
36 conjugacy classes of subgroups.
260 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C25×#66526, C5×Dic5×#66526, C4×C52×#66526, … |
| maximal normal subgroup of | C4×C25×#66526, C4×C52×#66526 |
| maximal quotient of | C4×C25×#66526, C5×Dic5×#66526, C4×C52×#66526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 57);