Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#89850 |
| Hall | C3×C7 ⋊ #500 |
| Sylow | C7 ⋊ C3×#500 |
196 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 1344 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2,3)(4,5,7,9,10,8,6)(11,13,14,18)(12,15,16,17)(20,23)(21,26)(24,25);(11,12,14,16)(13,17,18,15);(5,6)(7,8)(9,10)(19,20,21,24,22,25,26,23)192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4800);