Finite Group DatabasebetaFinite Group Databasebeta| order | 25050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C167 · Schur multiplier (H2) = C1 |
| direct product | D75×C167 |
| unambiguous semidirect product | C3⋊(D25×C167) |
| unambiguous semidirect product | C25⋊(D3×C167) |
| Fitting, Hall | C3×C25×C167 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C2×C167 |
| Hall | C25×C167 ⋊ D3 |
| Hall | C3×C167 ⋊ D25 |
| Sylow | C25 ⋊ D3×C167 |
| Sylow | C3 ⋊ D25×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C2×C167 |
| Frattini | C5 | D15×C167 |
| Fitting | C3×C25×C167 | C2 |
| socle | C3×C5×C167 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C167 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12525 |
6513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25050, 7);