Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | D3×C7×#104 |
| Fitting | C3×C7×#104 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#104 |
| Sylow | C3 ⋊ C2×C7×#104 |
340 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×#453, D3×D7×#104, D3×#89594, … |
| maximal normal subgroup of | D3×C7×#453, D3×D7×#104, D3×#89594, … |
| maximal quotient of | C7×#10590393 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5144);