Finite Group DatabasebetaFinite Group Databasebeta| order | 8050 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23×C25 · Schur multiplier (H2) = C1 |
| direct product | D7×C23×C25 |
| unambiguous semidirect product | C7⋊(C2×C23×C25) |
| Fitting, Hall | C7×C23×C25 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C23×C25 |
| Hall | C7×C25 ⋊ C2×C23 |
| Hall | C7×C23 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C25 | D7 |
| commutator, hypocenter | C7 | C2×C23×C25 |
| Frattini | C5 | C5×D7×C23 |
| Fitting | C7×C23×C25 | C2 |
| socle | C5×C7×C23 | C2×C5 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C23×C25 | |
24 conjugacy classes of subgroups.
2875 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C25×D23, D7×C23×D25, D7×D575, … |
| maximal normal subgroup of | D7×C25×D23, D7×C23×D25, D7×D575, … |
| maximal quotient of | C23×C25×Dic7, C2×D7×C23×C25, C3×D7×C23×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8050, 3);