Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#5806 |
| Fitting | C22×C3×C7×D4 ⋊ C2 |
| Hall | C3×C7 ⋊ #546 |
| Sylow | C3 ⋊ C7×#546 |
668 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2,3,4,5,6,7)(8,9,10)(12,14);(16,20)(17,21);(15,17,18,21)(16,19,20,22);(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)(21,22)315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10811);