Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#90268 |
| Fitting | C3×C4×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ #550 |
| Sylow | C7 ⋊ C3×#550 |
624 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 672 |
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2,3)(4,5,7,9,10,8,6)(11,12,13,14);(15,17,18,21)(16,19,20,22);(15,16,18,20)(17,22,21,19);(5,6)(7,8)(9,10)(12,14)(17,21)(19,22)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10208);