Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #4513 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#4513 |
| Hall | C3×C7 ⋊ #365 |
| Sylow | C3 ⋊ C7×#365 |
84 conjugacy classes of subgroups.
| 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)(11,12,13,16,14,18,19,23,15,17,20,22,21,24,26,25);(9,10)(12,16,17,22)(13,19)(14,21)(18,25,24,23)(20,26)252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 584);