Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#4294⋊C2 |
| unambiguous semidirect product | #4294⋊(C2×C25) |
| derived, Sylow | C19 ⋊ C2×C9×C25 |
| Hall | C25×#4294 ⋊ C2 |
| Hall | C25×D19 ⋊ C9 |
| Hall | C19×C25 ⋊ C2×C9 |
| Hall | #4294 ⋊ C2×C25 |
| Hall | D19 ⋊ C9×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C9×C25 |
| Frattini | C3×C5 | C5×D19⋊C3 |
| Fitting | C3×C19×C25 | C2×C3 |
| socle | C3×C5×C19 | C2×C3×C5 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C25 | |
36 conjugacy classes of subgroups.
675 conjugacy classes — view the full character table.
| maximal subgroup of | D25×#4294⋊C2, C2×C25×#4294⋊C2 |
| maximal normal subgroup of | D25×#4294⋊C2, C2×C25×#4294⋊C2 |
| maximal quotient of | C25×#4294⋊C4, C2×C25×#4294⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 2);