Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | D8×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C22×D8)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C7×D8)⋊A4 |
| Fitting, Hall | C22×C7×D8 ⋊ C3 |
| Sylow | C22×D8 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ A4×D8 |
186 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10080);