Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C1 |
| direct product | Dic6×AGL(1,𝔽8) |
| unambiguous semidirect product | C3⋊(Q8×AGL(1,𝔽8)) |
| unambiguous semidirect product | (C3×AGL(1,𝔽8))⋊Q8 |
| unambiguous semidirect product | (C23×Dic6)⋊C7 |
| Hall | C23×Dic6 ⋊ C7 |
| Sylow | C3 ⋊ Q8×AGL(1,𝔽8) |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11311);