Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D7×A4⋊Q8 |
| unambiguous semidirect product | (A4×D7)⋊Q8 |
| Sylow | C7 ⋊ C2×A4⋊Q8 |
330 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11320);