Finite Group DatabasebetaFinite Group Databasebeta| order | 10850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C7⋊(D31⋊C5)) |
| unambiguous semidirect product | C7⋊(C5⋊(D31⋊C5)) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D35 |
| unambiguous semidirect product | D1085⋊C5 |
| Fitting, socle, derived | C5×C7×C31 ⋊ C2×C5 |
| Hall | C5×C7×ΓL(1,𝔽32) ⋊ C2 |
| Hall | C5×ΓL(1,𝔽32) ⋊ D7 |
| Hall | C7×C31 ⋊ C5×D5 |
| Sylow | C31 ⋊ C5×D35 |
| Sylow | C7 ⋊ C5⋊(D31⋊C5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C31 | C2×C5 |
| LCS | G ▷ C5×C7×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,7,31|c^a=c^4,d^a=d^6,e^a=e^30,e^b=e^16200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10850, 19);