Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×D7×C25 |
| Fitting, Hall | C3×C7×C25 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C3×C25 |
| Hall | C7×C25 ⋊ C2×C3 |
| Hall | C3×C7 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | D7 |
| commutator, hypocenter | C7 | C2×C3×C25 |
| Frattini | C5 | C3×C5×D7 |
| Fitting | C3×C7×C25 | C2 |
| socle | C3×C5×C7 | C2×C5 |
| prime radical | C3×C5×D7 | C5 |
| cosocle | C5×C7 | C2×C3×C5 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 525 |
375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D25, D3×D7×C25, D7×D75, … |
| maximal normal subgroup of | C3×D7×D25, D3×D7×C25, D7×D75, … |
| maximal quotient of | C3×C25×Dic7, C2×C3×D7×C25, C9×D7×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 5);