Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#6470⋊C3 |
| unambiguous semidirect product | (C2×#6470)⋊C3 |
| Fitting | C2×C7×M16 ⋊ C2×C3 |
| Hall | C2×#6470 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#131 |
| Sylow | C7 ⋊ C2×C3×#131 |
532 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6767);