Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | C2×C52⋊#4296 |
| unambiguous semidirect product | (C2×C52)⋊#4296 |
| Fitting, socle, Hall | C2×C52×C19 ⋊ C9 |
| derived, Hall | C52×C19 ⋊ C2×C9 |
| Hall | C2×C52 ⋊ #4296 |
| Hall | C2×C19 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ C2×#4296 |
| Sylow | C19 ⋊ C2×C52⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C52⋊#4296 |
| commutator, hypocenter | C52×C19 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C19 | C9 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
166 conjugacy classes — view the full character table.
| maximal subgroup of | #30685637, #1039⋊#4296, #30685641, … |
| maximal normal subgroup of | #30685637, #1039⋊#4296, #30685641, … |
| maximal quotient of | C4×C52⋊#4296, C22×C52⋊#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 80);