Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | M16×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C22×M16)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C7×M16)⋊A4 |
| Fitting, Hall | C22×C7×M16 ⋊ C3 |
| Sylow | C22×M16 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ A4×M16 |
166 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10077);