Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D539 |
| unambiguous semidirect product | C49⋊(D11×C25) |
| Fitting, Hall | C11×C25×C49 ⋊ C2 |
| derived, Hall | C11×C49 ⋊ C2×C25 |
| Hall | C25×C49 ⋊ D11 |
| Hall | C11×C25 ⋊ D49 |
| Sylow | C49 ⋊ D11×C25 |
| Sylow | C11 ⋊ C25×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D539 |
| commutator, hypocenter | C11×C49 | C2×C25 |
| Frattini | C5×C7 | C5×D77 |
| Fitting | C11×C25×C49 | C2 |
| socle | C5×C7×C11 | C5×D7 |
| prime radical | C5×D539 | C5 |
| cosocle | C5×C11×C49 | C2×C5 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
6775 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 8);