Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C37 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×D5×C37 |
| unambiguous semidirect product | (C5×D3)⋊(C2×C3×C37) |
| unambiguous semidirect product | (C3×D5)⋊(C2×C3×C37) |
| unambiguous semidirect product | D15⋊(C2×C3×C37) |
| Fitting, socle, Hall | C32×C5×C37 ⋊ C22 |
| derived | C3×C5 ⋊ C22×C3×C37 |
| Hall | C32×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×C3×D3 |
| Hall | C32×C5 ⋊ C22×C37 |
| Sylow | C32 ⋊ C2×D5×C37 |
| Sylow | C5 ⋊ C2×C3×D3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | D3×D5 |
| commutator, hypocenter | C3×C5 | C22×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C37 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C37 | |
88 conjugacy classes of subgroups.
1332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C37×D25, C3×C5×D3×D5×C37, C3×D5×D15×C37, … |
| maximal normal subgroup of | C3×C5×D3×D5×C37 |
| maximal quotient of | C3×D3×C37×D25, C3×C5×D3×D5×C37, C3×D5×D15×C37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 132);