Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | Q8×AΓL(1,𝔽8) |
| unambiguous semidirect product | AGL(1,𝔽8)⋊(C3×Q8) |
| Fitting, Sylow | C23×Q8 ⋊ ΓL(1,𝔽8) |
| Hall | Q8×AGL(1,𝔽8) ⋊ C3 |
111 conjugacy classes of subgroups.
| transitive degree | μt(G) = 56 |
40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11308);