Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×#15668133 |
| Fitting, socle | C3×C52×C19 ⋊ C2×C3 |
| derived, Hall | C52×C19 ⋊ C2×C32 |
| Hall | C3×C19⋊(C52⋊C3) ⋊ C2 |
| Hall | C5⋊D95 ⋊ C32 |
| Sylow | C52 ⋊ C3×D19⋊C3 |
| Sylow | C19 ⋊ C3×(C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15668133 |
| commutator, hypocenter | C52×C19 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C2×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
255 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D19⋊((C5⋊D5)⋊C3), D3×#15668133, #15668133⋊D3, … |
| maximal normal subgroup of | C3×D19⋊((C5⋊D5)⋊C3), D3×#15668133, #15668133⋊D3, … |
| maximal quotient of | C3×#19152793, C2×C3×#15668133 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 90);