Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#90238 |
| Fitting | C3×C4×C7×D4 ⋊ C2 |
| Hall | C3×C7 ⋊ #525 |
| Sylow | C7 ⋊ C3×#525 |
660 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)(4,5,7,9,10,8,6)(12,14)(16,20)(19,22);(15,17,18,21)(16,19,20,22);(11,12)(13,14);(5,6)(7,8)(9,10)(15,16)(17,19)(18,20)(21,22)264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10181);