Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| isoclinism | isoclinic class of D171 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D171 |
| unambiguous semidirect product | C9⋊(C25×D19) |
| unambiguous semidirect product | C19⋊(D9×C25) |
| Fitting, Hall | C9×C19×C25 ⋊ C2 |
| derived, Hall | C9×C19 ⋊ C2×C25 |
| Hall | C19×C25 ⋊ D9 |
| Hall | C9×C25 ⋊ D19 |
| Sylow | C19 ⋊ D9×C25 |
| Sylow | C9 ⋊ C25×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D171 |
| commutator, hypocenter | C9×C19 | C2×C25 |
| Frattini | C3×C5 | C5×D57 |
| Fitting | C9×C19×C25 | C2 |
| socle | C3×C5×C19 | C5×D3 |
| LCS | G ▷ C9×C19 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
2175 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C25×D19, D25×D171, D171⋊D25, … |
| maximal normal subgroup of | D9×C25×D19, D25×D171, D171⋊D25, … |
| maximal quotient of | C25×Dic171, C2×C25×D171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 10);