Finite Group DatabasebetaFinite Group Databasebeta| order | 11850 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D75 |
| unambiguous semidirect product | C3⋊(D25×C79) |
| unambiguous semidirect product | C25⋊(D3×C79) |
| Fitting, Hall | C3×C25×C79 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C2×C79 |
| Hall | C25×C79 ⋊ D3 |
| Hall | C3×C79 ⋊ D25 |
| Sylow | C25 ⋊ D3×C79 |
| Sylow | C3 ⋊ D25×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C2×C79 |
| Frattini | C5 | D15×C79 |
| Fitting | C3×C25×C79 | C2 |
| socle | C3×C5×C79 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C79 | |
24 conjugacy classes of subgroups.
3081 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D75×D79, D3×D25×C79, D75⋊D79, … |
| maximal normal subgroup of | D75×D79, D3×D25×C79, D75⋊D79, … |
| maximal quotient of | C79×Dic75, C2×C79×D75, C79×D225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11850, 8);