Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of D175 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D175 |
| unambiguous semidirect product | C25⋊(C3×D7) |
| Fitting, Hall | C3×C7×C25 ⋊ C2 |
| derived, Hall | C7×C25 ⋊ C2×C3 |
| Hall | C3×C25 ⋊ D7 |
| Sylow | C25 ⋊ C3×D7 |
| Hall | C3×C7 ⋊ D25 |
| Sylow | C7 ⋊ C3×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D175 |
| commutator, cosocle, hypocenter | C7×C25 | C2×C3 |
| Frattini | C5 | C3×D35 |
| Fitting | C3×C7×C25 | C2 |
| socle | C3×C5×C7 | D5 |
| LCS | G ▷ C7×C25 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 525 |
267 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D25, D3×D175, D21⋊D25, … |
| maximal normal subgroup of | C3×D7×D25, D3×D175, D21⋊D25, … |
| maximal quotient of | C3×Dic175, C2×C3×D175, C9×D175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 7);