Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| isoclinism | isoclinic class of D195 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D195 |
| unambiguous semidirect product | C3⋊(C3×C5×D65) |
| unambiguous semidirect product | C5⋊(C3×C5×D39) |
| Fitting, socle, Hall | C32×C52×C13 ⋊ C2 |
| derived | C3×C5×C13 ⋊ C2×C3×C5 |
| Hall | C52×C13 ⋊ C3×D3 |
| Hall | C32×C52 ⋊ D13 |
| Hall | C32×C13 ⋊ C5×D5 |
| Sylow | C52 ⋊ C3×D39 |
| Sylow | C13 ⋊ C3×C5×D15 |
| Sylow | C32 ⋊ C5×D65 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D195 |
| commutator, hypocenter | C3×C5×C13 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C13 | C2 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 ◁ C3×C5 | |
96 conjugacy classes of subgroups.
1485 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D13×D15, C3×C5×D5×D39, C3×C5×D3×D65, … |
| maximal normal subgroup of | C3×C5×D13×D15, C3×C5×D5×D39, C3×C5×D3×D65, … |
| maximal quotient of | C3×C5×Dic195, C2×C3×C5×D195 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 108);