Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic5×#66526 |
| derived, Hall | C5×C37 ⋊ C4×C9 |
| Hall | C5×#66526 ⋊ C4 |
| Hall | Dic5×C37 ⋊ C9 |
| Sylow | C37 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ C4×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×#66526 |
| commutator, hypocenter | C5×C37 | C4×C9 |
| Fitting, socle | C2×C5×C37 | C2×C9 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
104 conjugacy classes — view the full character table.
| maximal subgroup of | Dic25×#66526, C5×Dic5×#66526, #1039×#66526, … |
| maximal normal subgroup of | C5×Dic5×#66526 |
| maximal quotient of | Dic25×#66526, C5×Dic5×#66526, #1039×#66526, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 56);