Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C19⋊#3874 |
| Fitting, socle | C3×C52×C19 ⋊ D3 |
| derived | C19×C52⋊C3 ⋊ C2×C3 |
| Hall | C3×C19×C52⋊C3 ⋊ C2 |
| Hall | C52×C19 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ D19 |
| Sylow | C52 ⋊ C3×D57 |
| Sylow | C19 ⋊ C3×#3874 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊#3874 |
| commutator, hypocenter | C19×C52⋊C3 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | D3 |
| LCS | G ▷ C19×C52⋊C3 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
336 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#3874⋊D19, C3×((C5⋊D5)⋊C3)⋊D19, C3×D19×#3874, … |
| maximal normal subgroup of | C3×#3874⋊D19, C3×((C5⋊D5)⋊C3)⋊D19, C3×D19×#3874, … |
| maximal quotient of | C3×C19⋊#64470, C2×C3×C19⋊#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 88);