Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D25×C19⋊C3 |
| unambiguous semidirect product | C25⋊(C2×C3×C19⋊C3) |
| unambiguous semidirect product | (C19×D25)⋊C32 |
| unambiguous semidirect product | (C3×C19×D25)⋊C3 |
| Fitting | C3×C19×C25 ⋊ C2×C3 |
| derived, Hall | C19×C25 ⋊ C2×C32 |
| Hall | C3×C25×C19⋊C3 ⋊ C2 |
| Hall | C19×D25 ⋊ C32 |
| Sylow | C25 ⋊ C2×C3×C19⋊C3 |
| Sylow | C19 ⋊ C32×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×C19⋊C3 |
| commutator, hypocenter | C19×C25 | C2×C32 |
| Frattini | C5 | C3×D5×C19⋊C3 |
| Fitting | C3×C19×C25 | C2×C3 |
| socle | C3×C5×C19 | C3×D5 |
| LCS | G ▷ C19×C25 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 19);