Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D25 |
| unambiguous semidirect product | C25⋊(C2×C3×C7) |
| Fitting, Hall | C3×C7×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C3×C7 |
| Hall | C7×C25 ⋊ C2×C3 |
| Hall | C3×C25 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C3×C7 |
| Frattini | C5 | C3×C7×D5 |
| Fitting | C3×C7×C25 | C2 |
| socle | C3×C5×C7 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C3×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 525 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×#1035, C3×C7⋊#1035, C7×C3⋊#1035, … |
| maximal normal subgroup of | C3×C7×#1035, C3×C7⋊#1035, C7×C3⋊#1035, … |
| maximal quotient of | C3×C7×Dic25, C2×C3×C7×D25, C7×C9×D25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 6);