Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C2 |
| direct product | C7×#4514 |
| Fitting | C3×C7×M32 ⋊ C2 |
| Hall | C3×C7 ⋊ #349 |
| Sylow | C3 ⋊ C7×#349 |
116 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 336 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5,6,7)(8,9,10)(11,12,13,17,14,18,20,24,15,16,19,22,21,23,25,26);(9,10)(12,16)(13,19)(18,23)(20,25)294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 585);