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×#89289 |
| 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)(11,13,14,19,17,22,16,12)(15,24,23,26,25,18,20,21);(5,6)(7,8)(9,10)(11,12,15,18,16,13,20,21,17,19,25,24,14,22,23,26)174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 443);