Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×(C2×S4)⋊C4 |
| unambiguous semidirect product | (C2×S4)⋊(C4×C7) |
| Fitting | C23×C4×C7 ⋊ D3 |
286 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 46 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)(8,9,10,11)(13,15)(16,17,19);(12,13)(14,15)(17,18)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6422);