Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C19⋊C3×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C5⋊D5×C19⋊C3)⋊C3 |
| unambiguous semidirect product | (C19×(C5⋊D5)⋊C3)⋊C3 |
| unambiguous semidirect product | ((C5⋊D5)⋊(C19⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C52×C19 ⋊ C2×C32 |
| Hall | C19⋊C3×C52⋊C3 ⋊ C2 |
| Hall | C19×C5⋊D5 ⋊ C32 |
| Hall | C5⋊D5 ⋊ C3×C19⋊C3 |
| Sylow | C52 ⋊ C2×C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×(C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C19 | C2×C32 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 76);