Finite Group DatabasebetaFinite Group Databasebeta| order | 10950 |
| isoclinism | isoclinic class of D73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D73⋊C3 |
| unambiguous semidirect product | D73⋊(C3×C25) |
| unambiguous semidirect product | (C73⋊C3)⋊(C2×C25) |
| unambiguous semidirect product | (C25×D73)⋊C3 |
| Fitting, Hall | C25×C73 ⋊ C2×C3 |
| derived, Sylow | C73 ⋊ C2×C3×C25 |
| Hall | C25×C73⋊C3 ⋊ C2 |
| Hall | C25×D73 ⋊ C3 |
| Hall | C73⋊C3 ⋊ C2×C25 |
| Hall | D73 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D73⋊C3 |
| commutator, hypocenter | C73 | C2×C3×C25 |
| Frattini | C5 | C5×D73⋊C3 |
| Fitting | C25×C73 | C2×C3 |
| socle, cosocle | C5×C73 | C2×C3×C5 |
| prime radical | C5×D73⋊C3 | C5 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
450 conjugacy classes — view the full character table.
| maximal subgroup of | C25×#64408⋊C3, #20300472⋊C3, D25×D73⋊C3, … |
| maximal normal subgroup of | C25×#64408⋊C3, #20300472⋊C3, D25×D73⋊C3, … |
| maximal quotient of | C25×Dic73⋊C3, C2×C25×D73⋊C3, C25×#10620321⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10950, 10);