Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#5416 |
140 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 140 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) = 27 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5,6,7)(8,9,11)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(9,10)(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6425);