Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #89282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#89282 |
| 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)(12,16,17,18)(13,20)(14,22)(19,25,23,24)(21,26);(5,6)(7,8)(9,10)(11,12,13,18,14,19,20,25,15,17,21,16,22,23,26,24)174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 436);