Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #89308 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#89308 |
| Hall | C3×C7 ⋊ #365 |
| Sylow | C7 ⋊ C3×#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)(4,5,7,9,10,8,6)(11,12,13,16,14,18,19,23,15,17,20,22,21,24,26,25);(5,6)(7,8)(9,10)(12,16,17,22)(13,19)(14,21)(18,25,24,23)(20,26)228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 462);