Finite Group DatabasebetaFinite Group Databasebeta| order | 950 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D19 |
| unambiguous semidirect product | C19⋊(C2×C25) |
| Fitting, Hall | C19×C25 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D19 |
| commutator, hypocenter | C19 | C2×C25 |
| Frattini | C5 | C5×D19 |
| Fitting | C19×C25 | C2 |
| socle, cosocle | C5×C19 | C2×C5 |
| prime radical | C5×D19 | C5 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 475 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D25, C2×C25×D19, C25×D19⋊C3, … |
| maximal normal subgroup of | D19×D25, C2×C25×D19, C25×D19⋊C3, … |
| maximal quotient of | C25×Dic19, C2×C25×D19, C3×C25×D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(950, 2);