Finite Group DatabasebetaFinite Group Databasebeta| order | 3850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D275 |
| unambiguous semidirect product | C11⋊(C7×D25) |
| unambiguous semidirect product | C25⋊(C7×D11) |
| Fitting, Hall | C7×C11×C25 ⋊ C2 |
| derived, Hall | C11×C25 ⋊ C2×C7 |
| Hall | C7×C25 ⋊ D11 |
| Hall | C7×C11 ⋊ D25 |
| Sylow | C25 ⋊ C7×D11 |
| Sylow | C11 ⋊ C7×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D275 |
| commutator, cosocle, hypocenter | C11×C25 | C2×C7 |
| Frattini | C5 | C7×D55 |
| Fitting | C7×C11×C25 | C2 |
| socle | C5×C7×C11 | D5 |
| LCS | G ▷ C11×C25 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1925 |
973 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D275, C7×D825, ΓL(1,𝔽8)×D275, … |
| maximal normal subgroup of | C3×C7×D275, ΓL(1,𝔽8)×D275, C49×D275, … |
| maximal quotient of | C3×C7×D275, C7×D825, C49×D275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3850, 10);