Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#4516 |
| Fitting | C3×C7×M32 ⋊ C2 |
| Hall | C3×C7 ⋊ #361 |
| Sylow | C3 ⋊ C7×#361 |
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 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)(11,12,13,20,21,23,26,24,15,17,22,16,14,18,19,25);(9,10)(12,16)(13,19)(14,21)(17,20)(18,25)(22,26)(23,24)252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 587);