Finite Group DatabasebetaFinite Group Databasebeta| order | 8850 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25×C59 · Schur multiplier (H2) = C1 |
| direct product | D3×C25×C59 |
| unambiguous semidirect product | C3⋊(C2×C25×C59) |
| Fitting, Hall | C3×C25×C59 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C25×C59 |
| Hall | C3×C59 ⋊ C2×C25 |
| Hall | C3×C25 ⋊ C2×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C59 | D3 |
| commutator, hypocenter | C3 | C2×C25×C59 |
| Frattini | C5 | C5×D3×C59 |
| Fitting | C3×C25×C59 | C2 |
| socle | C3×C5×C59 | C2×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C25×C59 | |
24 conjugacy classes of subgroups.
4425 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C25×D59, D3×D25×C59, D3×D1475, … |
| maximal normal subgroup of | D3×C25×D59, D3×D25×C59, D3×D1475, … |
| maximal quotient of | Dic3×C25×C59, C2×D3×C25×C59, D9×C25×C59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8850, 5);