Finite Group DatabasebetaFinite Group Databasebeta| order | 11850 |
| isoclinism | isoclinic class of D237 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D237 |
| unambiguous semidirect product | C3⋊(C25×D79) |
| unambiguous semidirect product | C79⋊(D3×C25) |
| Fitting, Hall | C3×C25×C79 ⋊ C2 |
| derived, Hall | C3×C79 ⋊ C2×C25 |
| Hall | C25×C79 ⋊ D3 |
| Sylow | C79 ⋊ D3×C25 |
| Hall | C3×C25 ⋊ D79 |
| Sylow | C3 ⋊ C25×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D237 |
| commutator, hypocenter | C3×C79 | C2×C25 |
| Frattini | C5 | C5×D237 |
| Fitting | C3×C25×C79 | C2 |
| socle, cosocle | C3×C5×C79 | C2×C5 |
| prime radical | C5×D237 | C5 |
| LCS | G ▷ C3×C79 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
3000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C25×D79, D25×D237, D75⋊D79, … |
| maximal normal subgroup of | D3×C25×D79, D25×D237, D75⋊D79, … |
| maximal quotient of | C25×Dic237, C2×C25×D237, C25×D711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11850, 7);