Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×D7×ΓL(1,𝔽32) |
| unambiguous semidirect product | C7⋊(C2×C5×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (D7×C31)⋊C52 |
| unambiguous semidirect product | (C5×D7×C31)⋊C5 |
| Fitting, socle | C5×C7×C31 ⋊ C2×C5 |
| derived, Hall | C7×C31 ⋊ C2×C52 |
| Hall | C5×C7×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D7×C31 ⋊ C52 |
| Sylow | C31 ⋊ C52×D7 |
| Sylow | C7 ⋊ C2×C5×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D7×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C7×C31 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C31 | C2×C5 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C5 | |
64 conjugacy classes of subgroups.
275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 16);