Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D21 |
| unambiguous semidirect product | C3⋊(D7×C25) |
| unambiguous semidirect product | C7⋊(D3×C25) |
| Fitting, Hall | C3×C7×C25 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C2×C25 |
| Hall | C7×C25 ⋊ D3 |
| Hall | C3×C25 ⋊ D7 |
| Sylow | C7 ⋊ D3×C25 |
| Sylow | C3 ⋊ D7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D21 |
| commutator, hypocenter | C3×C7 | C2×C25 |
| Frattini | C5 | C5×D21 |
| Fitting | C3×C7×C25 | C2 |
| socle, cosocle | C3×C5×C7 | C2×C5 |
| prime radical | C5×D21 | C5 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 525 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D7×C25, D21×D25, D21⋊D25, … |
| maximal normal subgroup of | D3×D7×C25, D21×D25, D21⋊D25, … |
| maximal quotient of | C25×Dic21, C2×C25×D21, C25×D63, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 9);