Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C3×#6503 |
| Fitting | C22×C3×C7×D4 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#127 |
| Sylow | C7 ⋊ C2×C3×#127 |
996 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10425);