Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×C22⋊#66526 |
| unambiguous semidirect product | C22⋊(C5×#66526) |
| unambiguous semidirect product | (C22×C5)⋊#66526 |
| Fitting, socle, Hall | C22×C5×C37 ⋊ C9 |
| derived, Hall | C22×C37 ⋊ C5×C9 |
| Hall | C5×C37 ⋊ C22⋊C9 |
| Sylow | C37 ⋊ C5×C22⋊C9 |
| Hall | C22×C5 ⋊ #66526 |
| Sylow | C22 ⋊ C5×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C22⋊#66526 |
| commutator, hypocenter | C22×C37 | C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C37 | C9 |
| LCS | G ▷ C22×C37 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
140 conjugacy classes — view the full character table.
| maximal subgroup of | C25×C22⋊#66526, C52×C22⋊#66526 |
| maximal normal subgroup of | C25×C22⋊#66526, C52×C22⋊#66526 |
| maximal quotient of | C25×C22⋊#66526, C52×C22⋊#66526 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 108);