Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C37 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×C3⋊D3×C37 |
| unambiguous semidirect product | (C3×D5)⋊(D3×C37) |
| Fitting, socle, Hall | C32×C5×C37 ⋊ C22 |
| derived, Hall | C32×C5 ⋊ C22×C37 |
| Hall | C32×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D5×C37 |
| Sylow | C5 ⋊ C2×C3⋊D3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D5×C3⋊D3 |
| commutator, hypocenter | C32×C5 | C22×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C37 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C37 | |
120 conjugacy classes of subgroups.
888 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×C37×D25, C5×D5×C3⋊D3×C37, D5×C37×C3⋊D15, … |
| maximal normal subgroup of | C5×D5×C3⋊D3×C37 |
| maximal quotient of | C3⋊D3×C37×D25, C5×D5×C3⋊D3×C37, D5×C37×C3⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 144);