Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#89419 |
| Hall | C3×C7 ⋊ #389 |
| Sylow | C7 ⋊ C3×#389 |
340 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 1344 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3)(4,5,7,9,10,8,6)(11,12,13,14)(16,18)(19,21,22,20);(15,16,17,18)(20,21);(5,6)(7,8)(9,10)(19,20,22,21)264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4381);