Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×Q64 |
| unambiguous semidirect product | (C7×Q64)⋊C3 |
| Fitting, Hall | C7×Q64 ⋊ C3 |
| Sylow | C7 ⋊ C3×Q64 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 390);