Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×#919 |
| Fitting | C2×C3×C7×Q16 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#135 |
| Sylow | C3 ⋊ C2×C7×#135 |
532 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10770);