Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of Dic42 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#66631 |
| Fitting | C2×C3×C42×C7 ⋊ C2 |
| Hall | C3×C7 ⋊ C4×C22⋊C4 |
| Sylow | C7 ⋊ C4×(C2×D3)⋊C4 |
| Sylow | C3 ⋊ C4×(C2×D7)⋊C4 |
516 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5864);