Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #4487 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#4494 |
| 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)(11,13,14,19,17,22,16,12)(15,24,23,26,25,18,20,21);(9,10)(11,12,15,18,16,13,20,21,17,19,25,24,14,22,23,26)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 565);