Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | #108×D21 |
| Fitting | C3×C7×#108 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#108 |
| Sylow | C7 ⋊ D3×#108 |
| Sylow | C3 ⋊ D7×#108 |
212 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5818);