Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C3⋊C8×Dic14 |
| Hall | C3×C7 ⋊ C8×Q8 |
| Sylow | C7 ⋊ Q8×C3⋊C8 |
| Sylow | C3 ⋊ C8×Dic14 |
204 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1344 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1512);