Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×C7⋊C8 |
| derived, Hall | C3×C7 ⋊ C23×C8 |
| Sylow | C7 ⋊ C22×D3×C8 |
| Sylow | C3 ⋊ C23×C7⋊C8 |
676 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 352 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 8707);