Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D775 |
| unambiguous semidirect product | C25⋊(C7×D31) |
| unambiguous semidirect product | C31⋊(C7×D25) |
| Fitting, Hall | C7×C25×C31 ⋊ C2 |
| derived, Hall | C25×C31 ⋊ C2×C7 |
| Hall | C7×C31 ⋊ D25 |
| Hall | C7×C25 ⋊ D31 |
| Sylow | C31 ⋊ C7×D25 |
| Sylow | C25 ⋊ C7×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D775 |
| commutator, cosocle, hypocenter | C25×C31 | C2×C7 |
| Frattini | C5 | C7×D155 |
| Fitting | C7×C25×C31 | C2 |
| socle | C5×C7×C31 | D5 |
| LCS | G ▷ C25×C31 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
2723 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D25×D31, D7×D775, D175⋊D31, … |
| maximal normal subgroup of | C7×D25×D31, D7×D775, D175⋊D31, … |
| maximal quotient of | C7×Dic775, C2×C7×D775, C3×C7×D775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 7);