Finite Group DatabasebetaFinite Group Databasebeta| order | 22308 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C11⋊AGL(1,𝔽13) |
| unambiguous semidirect product | C11⋊(C13×AGL(1,𝔽13)) |
| unambiguous semidirect product | (C11⋊#261)⋊(C3×C13) |
| Fitting, socle, Hall | C11×C132 ⋊ C3×C4 |
| derived | C11×C13 ⋊ C3×C4×C13 |
| Hall | C13×C11⋊#261 ⋊ C3 |
| Hall | C11×C13×C13⋊C3 ⋊ C4 |
| Hall | C13×C13⋊C3 ⋊ Dic11 |
| Sylow | C132 ⋊ C3×Dic11 |
| Sylow | C11 ⋊ C13×AGL(1,𝔽13) |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1716 |
689 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22308, 100);