Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#89548 |
| Fitting | C3×C7×#102 ⋊ C2 |
| Hall | C3×C7 ⋊ #450 |
| Sylow | C7 ⋊ C3×#450 |
376 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 336 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3)(4,5,7,9,10,8,6)(11,12,13,14)(15,16,18,20)(17,22,21,19);(16,19)(17,21)(20,22);(5,6)(7,8)(9,10)(12,14)183 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4505);