Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1425 |
| unambiguous semidirect product | C3⋊(C3×D475) |
| unambiguous semidirect product | C25⋊(C3×D57) |
| Fitting, Hall | C32×C19×C25 ⋊ C2 |
| derived | C3×C19×C25 ⋊ C2×C3 |
| Hall | C19×C25 ⋊ C3×D3 |
| Hall | C32×C25 ⋊ D19 |
| Hall | C32×C19 ⋊ D25 |
| Sylow | C25 ⋊ C3×D57 |
| Sylow | C19 ⋊ C3×D75 |
| Sylow | C32 ⋊ D475 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1425 |
| commutator, hypocenter | C3×C19×C25 | C2×C3 |
| Frattini | C5 | C3×D285 |
| Fitting | C32×C19×C25 | C2 |
| socle | C32×C5×C19 | D5 |
| LCS | G ▷ C3×C19×C25 | |
| UCS | C1 ◁ C3 | |
54 conjugacy classes of subgroups.
2142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D75, C3×D25×D57, C3×D3×D475, … |
| maximal normal subgroup of | C3×D19×D75, C3×D25×D57, C3×D3×D475, … |
| maximal quotient of | C3×Dic1425, C2×C3×D1425 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 32);