Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D333 |
| unambiguous semidirect product | (C9×D5)⋊D37 |
| unambiguous semidirect product | (D5×C37)⋊D9 |
| Fitting, derived, Hall | C5×C9×C37 ⋊ C22 |
| Hall | C9×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D37 |
| Sylow | C37 ⋊ D5×D9 |
| Sylow | C9 ⋊ D5×D37 |
| Sylow | C5 ⋊ C2×D333 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C37 | C22 |
| Frattini | C3 | D5×D111 |
| socle | C3×C5×C37 | C2×D3 |
| LCS | G ▷ C5×C9×C37 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
672 conjugacy classes — view the full character table.
| maximal subgroup of | D25×D333, C5×D5×D333, C5⋊D5×D333, … |
| maximal normal subgroup of | C5×D5×D333 |
| maximal quotient of | D25×D333, C5×D5×D333, C5⋊D5×D333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 40);