Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D3×C7×C8 |
| Fitting | C3×C4×C7×C8 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C4×C7×C8 |
| Hall | C3×C7 ⋊ C2×C4×C8 |
324 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 324 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 |
672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C4×D3×C7×C8 |
| maximal normal subgroup of | C3×C4×D3×C7×C8 |
| maximal quotient of | C3×C4×D3×C7×C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5008);