Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | D49×C11⋊C25 |
| unambiguous semidirect product | C49⋊(C2×C11⋊C25) |
| unambiguous semidirect product | (C11×D49)⋊C25 |
| derived, Hall | C11×C49 ⋊ C2×C25 |
| Hall | C49×C11⋊C25 ⋊ C2 |
| Hall | C11×D49 ⋊ C25 |
| Sylow | C49 ⋊ C2×C11⋊C25 |
| Sylow | C11 ⋊ C25×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊C5×D49 |
| commutator, hypocenter | C11×C49 | C2×C25 |
| Frattini | C5×C7 | D7×C11⋊C5 |
| Fitting, cosocle | C5×C11×C49 | C2×C5 |
| socle | C5×C7×C11 | C5×D7 |
| prime radical | C5×C11×D49 | C5 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
910 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 3);