Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | Q8×D7⋊A4 |
| unambiguous semidirect product | D7⋊(Q8×A4) |
| Fitting | C22×C7×Q8 ⋊ C2×C3 |
| Hall | C22×Q8×D7 ⋊ C3 |
| Sylow | C7 ⋊ C2×Q8×A4 |
410 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11478);