Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#89313 |
| Fitting | C3×C7×M32 ⋊ C2 |
| Hall | C3×C7 ⋊ #360 |
| Sylow | C7 ⋊ C3×#360 |
116 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3)(4,5,7,9,10,8,6)(11,13,21,12,16,23,14,18,17,24,20,19,15,26,25,22);(5,6)(7,8)(9,10)(11,12)(13,20)(14,23)(15,18)(16,22)(17,19)(21,24)(25,26)228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 467);