Finite Group DatabasebetaFinite Group Databasebeta| order | 7850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D785 |
| unambiguous semidirect product | C5⋊(C5×D157) |
| unambiguous semidirect product | C157⋊(C5×D5) |
| Fitting, socle, Hall | C52×C157 ⋊ C2 |
| derived | C5×C157 ⋊ C2×C5 |
| Sylow | C157 ⋊ C5×D5 |
| Sylow | C52 ⋊ D157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D785 |
| commutator, hypocenter | C5×C157 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C157 | C2 |
| LCS | G ▷ C5×C157 | |
| UCS | C1 ◁ C5 | |
20 conjugacy classes of subgroups.
1970 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#15691169, C5×#15691170, C5×D5×D157, … |
| maximal normal subgroup of | C5×#15691169, C5×#15691170, C5×D5×D157, … |
| maximal quotient of | C5×Dic785, C2×C5×D785, C3×C5×D785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7850, 8);