Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic333 |
| unambiguous semidirect product | C9⋊(C5×Dic37) |
| derived, Hall | C9×C37 ⋊ C4×C5 |
| Hall | C5×C9×C37 ⋊ C4 |
| Hall | C5×C37 ⋊ Dic9 |
| Hall | C5×C9 ⋊ Dic37 |
| Sylow | C37 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ C5×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D333 |
| commutator, hypocenter | C9×C37 | C4×C5 |
| Frattini | C2×C3 | C5×D111 |
| Fitting | C2×C5×C9×C37 | C2 |
| socle | C2×C3×C5×C37 | D3 |
| LCS | G ▷ C9×C37 | |
| UCS | C1 ◁ C2×C5 | |
36 conjugacy classes of subgroups.
1680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×Dic333, C52×Dic333, C5×Dic1665, … |
| maximal normal subgroup of | C25×Dic333, C52×Dic333 |
| maximal quotient of | C25×Dic333, C52×Dic333, C5×Dic1665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 10);