Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | Aut(G) order 2877120 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3330 |
| direct product | C2×D1665 |
| unambiguous semidirect product | (C2×C5)⋊D333 |
| unambiguous semidirect product | (C2×C9)⋊D185 |
| unambiguous semidirect product | (C2×C37)⋊D45 |
| Fitting | C2×C5×C9×C37 ⋊ C2 |
| derived, Hall | C5×C9×C37 ⋊ C22 |
| Hall | C9×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D45 |
| Sylow | C9 ⋊ C2×D185 |
| Sylow | C5 ⋊ C2×D333 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1665 |
| commutator, hypocenter | C5×C9×C37 | C22 |
| Frattini | C3 | C2×D555 |
| Fitting | C2×C5×C9×C37 | C2 |
| socle | C2×C3×C5×C37 | D3 |
| LCS | G ▷ C5×C9×C37 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
1668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D8325, D5×D1665, C2×C5⋊D1665, … |
| maximal normal subgroup of | C2×C5×D1665, D6660 |
| maximal quotient of | C2×D8325, D5×D1665, C2×C5⋊D1665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 52);