Finite Group DatabasebetaFinite Group Databasebeta| order | 8850 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C25×D59 |
| unambiguous semidirect product | C59⋊(C2×C3×C25) |
| Fitting, Hall | C3×C25×C59 ⋊ C2 |
| derived, Sylow | C59 ⋊ C2×C3×C25 |
| Hall | C25×C59 ⋊ C2×C3 |
| Hall | C3×C59 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | D59 |
| commutator, hypocenter | C59 | C2×C3×C25 |
| Frattini | C5 | C3×C5×D59 |
| Fitting | C3×C25×C59 | C2 |
| socle | C3×C5×C59 | C2×C5 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C3×C25 | |
24 conjugacy classes of subgroups.
2325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D25×D59, D3×C25×D59, D59×D75, … |
| maximal normal subgroup of | C3×D25×D59, D3×C25×D59, D59×D75, … |
| maximal quotient of | C3×C25×Dic59, C2×C3×C25×D59, C9×C25×D59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8850, 2);