Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| isoclinism | isoclinic class of D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C25×D57 |
| unambiguous semidirect product | C3⋊(C3×C25×D19) |
| Fitting, Hall | C32×C19×C25 ⋊ C2 |
| derived | C3×C19 ⋊ C2×C3×C25 |
| Hall | C19×C25 ⋊ C3×D3 |
| Hall | C32×C25 ⋊ D19 |
| Hall | C32×C19 ⋊ C2×C25 |
| Sylow | C19 ⋊ C3×D3×C25 |
| Sylow | C32 ⋊ C25×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | D57 |
| commutator, hypocenter | C3×C19 | C2×C3×C25 |
| Frattini | C5 | C3×C5×D57 |
| Fitting | C32×C19×C25 | C2 |
| socle | C32×C5×C19 | C2×C5 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C3×C25 | |
54 conjugacy classes of subgroups.
2250 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×C25×D19, C3×D25×D57, C3×D57⋊D25, … |
| maximal normal subgroup of | C3×D3×C25×D19, C3×D25×D57, C3×D57⋊D25, … |
| maximal quotient of | C3×C25×Dic57, C2×C3×C25×D57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 30);