Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#5817 |
| Fitting | C22×C3×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ #548 |
| Sylow | C3 ⋊ C7×#548 |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 672 |
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2,3,4,5,6,7)(8,9,10)(12,14);(15,17,18,21)(16,19,20,22);(15,16,18,20)(17,22,21,19);(9,10)(11,12)(13,14)(17,21)(19,22)315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10822);