Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C7×D31⋊C25 |
| unambiguous semidirect product | D31⋊(C7×C25) |
| unambiguous semidirect product | (C7×D31)⋊C25 |
| unambiguous semidirect product | (C31⋊C25)⋊(C2×C7) |
| derived, Sylow | C31 ⋊ C2×C7×C25 |
| Hall | C7×C31⋊C25 ⋊ C2 |
| Hall | C31⋊C25 ⋊ C2×C7 |
| Hall | C7×D31 ⋊ C25 |
| Hall | C7×C31 ⋊ C2×C25 |
| Hall | D31 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D31⋊C5 |
| commutator, hypocenter | C31 | C2×C7×C25 |
| Frattini | C5 | C7×D31⋊C5 |
| Fitting, socle | C5×C7×C31 | C2×C5 |
| prime radical | C5×C7×D31 | C5 |
| cosocle | C5×C31 | C2×C5×C7 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C5×C7 | |
24 conjugacy classes of subgroups.
455 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D31⋊C25, C2×C7×D31⋊C25, C3×C7×D31⋊C25, … |
| maximal normal subgroup of | D7×D31⋊C25, C2×C7×D31⋊C25, C3×C7×D31⋊C25, … |
| maximal quotient of | C7×Dic31⋊C25, C2×C7×D31⋊C25, C3×C7×D31⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 10);