Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C4⋊C4×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | C4⋊(C4×C22⋊ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C22×C4⋊C4)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C7×C4⋊C4)⋊A4 |
| Fitting, Hall | C22×C7×C4⋊C4 ⋊ C3 |
| Sylow | C22×C4⋊C4 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ A4×C4⋊C4 |
226 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10060);