Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #89246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#89280 |
| Fitting | C3×C7×C4⋊C8 ⋊ C2 |
| Hall | C3×C7 ⋊ #331 |
| Sylow | C7 ⋊ C3×#331 |
168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 26 points:
(1,2,3)(4,5,7,9,10,8,6)(11,12,13,16,14,15,17,18)(20,23)(21,26)(24,25);(5,6)(7,8)(9,10)(12,15)(13,17)(19,20)(21,23)(22,25)(24,26)237 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 432);