Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23 |
| direct product | D4×ΓL(1,𝔽8)⋊C8 |
| unambiguous semidirect product | (D4×C7⋊C8)⋊C3 |
| Hall | D4×C7⋊C8 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C8×D4 |
| Sylow | C7 ⋊ C3×C8×D4 |
268 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1199);