Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C4×AGL(1,𝔽8) |
| unambiguous semidirect product | (C24×C3×C4)⋊C7 |
| Fitting, Hall | C24×C3×C4 ⋊ C7 |
| derived | C23 ⋊ C2×C3×C4×C7 |
| Sylow | C24×C4 ⋊ C3×C7 |
254 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11371);