Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C3×D4×AGL(1,𝔽8) |
| unambiguous semidirect product | C4⋊(C2×C3×AGL(1,𝔽8)) |
| unambiguous semidirect product | (C23×C3×D4)⋊C7 |
| Fitting, Hall | C23×C3×D4 ⋊ C7 |
| Sylow | C23×D4 ⋊ C3×C7 |
254 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11372);