Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×D7×#97 |
| Fitting | C3×C7×#97 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#97 |
| Sylow | C7 ⋊ C2×C3×#97 |
292 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4428);