Finite Group DatabasebetaFinite Group Databasebeta| order | 10950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1825 |
| unambiguous semidirect product | C25⋊(C3×D73) |
| Fitting, Hall | C3×C25×C73 ⋊ C2 |
| derived, Hall | C25×C73 ⋊ C2×C3 |
| Hall | C3×C73 ⋊ D25 |
| Hall | C3×C25 ⋊ D73 |
| Sylow | C73 ⋊ C3×D25 |
| Sylow | C25 ⋊ C3×D73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1825 |
| commutator, cosocle, hypocenter | C25×C73 | C2×C3 |
| Frattini | C5 | C3×D365 |
| Fitting | C3×C25×C73 | C2 |
| socle | C3×C5×C73 | D5 |
| LCS | G ▷ C25×C73 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
2742 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20300469, C3×#20300470, C3×D25×D73, … |
| maximal normal subgroup of | C3×#20300469, C3×#20300470, C3×D25×D73, … |
| maximal quotient of | C3×Dic1825, C2×C3×D1825, C9×D1825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10950, 5);