Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#5417 |
| Fitting | C22×C7×Q8 ⋊ D3 |
154 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 168 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3,4,5,6,7)(8,9,11)(12,13,15,17)(14,19,18,16);(9,10)(13,16)(14,18)(17,19)133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6426);