Finite Group DatabasebetaFinite Group Databasebeta| order | 11850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1185 |
| unambiguous semidirect product | C3⋊(C5×D395) |
| unambiguous semidirect product | C5⋊(C5×D237) |
| unambiguous semidirect product | C79⋊(C5×D15) |
| Fitting, socle, Hall | C3×C52×C79 ⋊ C2 |
| derived | C3×C5×C79 ⋊ C2×C5 |
| Hall | C52×C79 ⋊ D3 |
| Hall | C3×C79 ⋊ C5×D5 |
| Sylow | C79 ⋊ C5×D15 |
| Hall | C3×C52 ⋊ D79 |
| Sylow | C52 ⋊ D237 |
| Sylow | C3 ⋊ C5×D395 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1185 |
| commutator, cosocle, hypocenter | C3×C5×C79 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C79 | C2 |
| LCS | G ▷ C3×C5×C79 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
2970 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D15×D79, C5×D5×D237, C5×D3×D395, … |
| maximal normal subgroup of | C5×D15×D79, C5×D5×D237, C5×D3×D395, … |
| maximal quotient of | C5×Dic1185, C2×C5×D1185, C5×D3555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11850, 32);