Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | A4×(C2×D7)⋊C4 |
| Fitting | C23×C4×C7 ⋊ C2×C3 |
| Hall | C22×(C2×D7)⋊C4 ⋊ C3 |
| Sylow | C7 ⋊ A4×C22⋊C4 |
338 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6898);