Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×C31⋊C25 |
| unambiguous semidirect product | (C2×C31)⋊(C7×C25) |
| unambiguous semidirect product | (C2×C7×C31)⋊C25 |
| derived, Sylow | C31 ⋊ C2×C7×C25 |
| Hall | C2×C7×C31 ⋊ C25 |
| Hall | C7×C31 ⋊ C2×C25 |
| Hall | C2×C31 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C7 | ΓL(1,𝔽32) |
| commutator, hypocenter | C31 | C2×C7×C25 |
| Frattini | C5 | C2×C7×ΓL(1,𝔽32) |
| Fitting, socle, prime radical | C2×C5×C7×C31 | C5 |
| cosocle | C5×C31 | C2×C5×C7 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C5×C7 | |
24 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 2);