Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D25×#4296 |
| unambiguous semidirect product | C25⋊(C2×#4296) |
| Fitting, derived, Hall | C19×C25 ⋊ C2×C9 |
| Hall | C25×#4296 ⋊ C2 |
| Hall | C19×D25 ⋊ C9 |
| Sylow | C25 ⋊ C2×#4296 |
| Sylow | C19 ⋊ C9×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C19×C25 | C2×C9 |
| Frattini | C5 | D5×#4296 |
| socle | C5×C19 | C9×D5 |
| LCS | G ▷ C19×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
154 conjugacy classes — view the full character table.
| maximal subgroup of | #4296⋊#1035, #1035×#4296, D25×AGL(1,𝔽19), … |
| maximal normal subgroup of | #4296⋊#1035, #1035×#4296, D25×AGL(1,𝔽19), … |
| maximal quotient of | Dic25×#4296, C2×D25×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 15);