Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#89436 |
| Fitting | C3×C7×#95 ⋊ C2 |
| Hall | C3×C7 ⋊ #381 |
| Sylow | C7 ⋊ C3×#381 |
436 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 672 |
A minimal faithful permutation representation — 3 generators on 26 points:
(1,2,3)(4,5,7,9,10,8,6)(11,12,13,14)(16,18)(20,24)(23,26);(15,16)(17,18)(19,21,22,25)(20,23,24,26);(5,6)(7,8)(9,10)(19,20)(21,23)(22,24)(25,26)264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4390);