Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic185⋊C3 |
| unambiguous semidirect product | Dic185⋊C32 |
| unambiguous semidirect product | (C3×Dic185)⋊C3 |
| derived, Hall | C5×C37 ⋊ C32×C4 |
| Hall | C3×C5×C37⋊C3 ⋊ C4 |
| Hall | Dic185 ⋊ C32 |
| Hall | C3×C37⋊C3 ⋊ Dic5 |
| Sylow | C37 ⋊ C32×Dic5 |
| Sylow | C5 ⋊ C3×Dic37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊(D37⋊C3) |
| commutator, hypocenter | C5×C37 | C32×C4 |
| Frattini | C2 | C3×C5⋊(D37⋊C3) |
| Fitting, socle | C2×C3×C5×C37 | C2×C3 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
252 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic925⋊C3, C3×C5×Dic185⋊C3, C3×#26012784, … |
| maximal normal subgroup of | C3×C5×Dic185⋊C3 |
| maximal quotient of | C3×Dic925⋊C3, C3×C5×Dic185⋊C3, C3×#26012784, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 59);