Finite Group DatabasebetaFinite Group Databasebeta| order | 8050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D575 |
| unambiguous semidirect product | C23⋊(C7×D25) |
| unambiguous semidirect product | C25⋊(C7×D23) |
| Fitting, Hall | C7×C23×C25 ⋊ C2 |
| derived, Hall | C23×C25 ⋊ C2×C7 |
| Hall | C7×C25 ⋊ D23 |
| Hall | C7×C23 ⋊ D25 |
| Sylow | C25 ⋊ C7×D23 |
| Sylow | C23 ⋊ C7×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D575 |
| commutator, hypocenter | C23×C25 | C2×C7 |
| Frattini | C5 | C7×D115 |
| Fitting | C7×C23×C25 | C2 |
| socle | C5×C7×C23 | D5 |
| LCS | G ▷ C23×C25 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
2023 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D23×D25, D7×D575, D161⋊D25, … |
| maximal normal subgroup of | C7×D23×D25, D7×D575, D161⋊D25, … |
| maximal quotient of | C7×Dic575, C2×C7×D575, C3×C7×D575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8050, 6);