Finite Group DatabasebetaFinite Group Databasebeta| order | 26949 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C691⋊C3 |
| unambiguous semidirect product | C691⋊(C3×C13) |
| Fitting, socle, Hall | C13×C691 ⋊ C3 |
| derived, Sylow | C691 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C691⋊C3 |
| commutator, cosocle, hypocenter | C691 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C691 | C3 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8983 |
3029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26949, 2);