Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| isoclinism | isoclinic class of D217 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D217 |
| unambiguous semidirect product | C7⋊(C25×D31) |
| Fitting, Hall | C7×C25×C31 ⋊ C2 |
| derived, Hall | C7×C31 ⋊ C2×C25 |
| Hall | C25×C31 ⋊ D7 |
| Hall | C7×C25 ⋊ D31 |
| Sylow | C31 ⋊ D7×C25 |
| Sylow | C7 ⋊ C25×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D217 |
| commutator, hypocenter | C7×C31 | C2×C25 |
| Frattini | C5 | C5×D217 |
| Fitting | C7×C25×C31 | C2 |
| socle, cosocle | C5×C7×C31 | C2×C5 |
| prime radical | C5×D217 | C5 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
2750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C25×D31, D25×D217, D175⋊D31, … |
| maximal normal subgroup of | D7×C25×D31, D25×D217, D175⋊D31, … |
| maximal quotient of | C25×Dic217, C2×C25×D217, C3×C25×D217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 5);