Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #89261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C1 |
| direct product | C3×#89307 |
| Hall | C3×C7 ⋊ #347 |
| Sylow | C7 ⋊ C3×#347 |
92 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)(11,12,13,18,14,16,20,23,15,17,19,24,21,22,26,25);(5,6)(7,8)(9,10)(12,16,17,22)(13,19)(18,25,24,23)(20,26)246 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 461);