Finite Group DatabasebetaFinite Group Databasebeta| order | 8550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle, derived, Hall | C52×C19 ⋊ C2×C32 |
| Hall | C19⋊C3×C52⋊C3 ⋊ C2 |
| Hall | C52×D19 ⋊ C32 |
| Hall | D19 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×D19⋊C3 |
| Sylow | C19 ⋊ C2×C3×C52⋊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.
99 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×#3874, D19⋊C3×(C5⋊D5)⋊C3, C2×C52⋊C3×D19⋊C3 |
| maximal normal subgroup of | D19⋊C3×#3874, D19⋊C3×(C5⋊D5)⋊C3, C2×C52⋊C3×D19⋊C3 |
| maximal quotient of | C52⋊C3×(C19⋊C3)⋊C4, C2×C52⋊C3×D19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8550, 78);