Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#13050613 |
| derived, Sylow | C37 ⋊ C4×C5×C9 |
| Hall | C5×#66524 ⋊ C4 |
| Hall | C5×#3866 ⋊ C9 |
| Hall | #66524 ⋊ C4×C5 |
| Hall | C5×C37 ⋊ C4×C9 |
| Hall | #3866 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #3866⋊C3 |
| commutator, hypocenter | C37 | C4×C5×C9 |
| Frattini | C3 | C5×#3866⋊C3 |
| Fitting, socle | C3×C5×C37 | C3×C4 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C5 | |
36 conjugacy classes of subgroups.
225 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#13050613, C52×#13050613, C5×#20269018, … |
| maximal normal subgroup of | C25×#13050613, C52×#13050613 |
| maximal quotient of | C25×#13050613, C52×#13050613, C5×#20269018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 14);