Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | Q8×C7⋊S4 |
| Fitting | C22×C7×Q8 ⋊ D3 |
| Sylow | C7 ⋊ Q8×S4 |
312 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
85 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11402);