Finite Group DatabasebetaFinite Group Databasebeta| order | 25950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C173 · Schur multiplier (H2) = C1 |
| direct product | D75×C173 |
| unambiguous semidirect product | C3⋊(D25×C173) |
| unambiguous semidirect product | C25⋊(D3×C173) |
| Fitting, Hall | C3×C25×C173 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C2×C173 |
| Hall | C25×C173 ⋊ D3 |
| Hall | C3×C173 ⋊ D25 |
| Sylow | C25 ⋊ D3×C173 |
| Sylow | C3 ⋊ D25×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C173 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C2×C173 |
| Frattini | C5 | D15×C173 |
| Fitting | C3×C25×C173 | C2 |
| socle | C3×C5×C173 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C173 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12975 |
6747 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25950, 7);