Finite Group DatabasebetaFinite Group Databasebeta| order | 8850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×D59 |
| unambiguous semidirect product | C59⋊(C2×C52⋊C3) |
| unambiguous semidirect product | (C52×D59)⋊C3 |
| Fitting, socle, derived, Hall | C52×C59 ⋊ C2×C3 |
| Hall | C59×C52⋊C3 ⋊ C2 |
| Hall | C52×D59 ⋊ C3 |
| Sylow | C59 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ C3×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C59 | C2×C3 |
| LCS | G ▷ C52×C59 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
341 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3874, D59×(C5⋊D5)⋊C3, C2×C52⋊C3×D59, … |
| maximal normal subgroup of | D59×#3874, D59×(C5⋊D5)⋊C3, C2×C52⋊C3×D59, … |
| maximal quotient of | C52⋊C3×Dic59, C2×C52⋊C3×D59, D59×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8850, 14);