Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C11⋊C5×D49 |
| unambiguous semidirect product | C49⋊(C2×C5×C11⋊C5) |
| unambiguous semidirect product | (C11×D49)⋊C52 |
| unambiguous semidirect product | (C5×C11×D49)⋊C5 |
| Fitting | C5×C11×C49 ⋊ C2×C5 |
| derived, Hall | C11×C49 ⋊ C2×C52 |
| Hall | C5×C49×C11⋊C5 ⋊ C2 |
| Hall | C11×D49 ⋊ C52 |
| Sylow | C49 ⋊ C2×C5×C11⋊C5 |
| Sylow | C11 ⋊ C52×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊C5×D49 |
| commutator, cosocle, hypocenter | C11×C49 | C2×C52 |
| Frattini | C7 | C5×D7×C11⋊C5 |
| Fitting | C5×C11×C49 | C2×C5 |
| socle | C5×C7×C11 | C5×D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C5 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2695 |
910 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 16);