Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | Q8×ΓL(1,𝔽8)⋊Q8 |
| Hall | Q8×Dic14 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ Q82 |
| Sylow | C7 ⋊ C3×Q82 |
424 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6589);