Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #4519 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#4519 |
| Fitting | C3×C7×D16 ⋊ C2 |
| Hall | C3×C7 ⋊ D32 |
| Sylow | C3 ⋊ C7×D32 |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 672 |
A minimal faithful permutation representation — 2 generators on 42 points:
(1,2,3,4,5,6,7)(8,9,10)(12,17)(13,22)(14,23)(15,27)(18,19)(20,36)(21,32)(24,41)(25,39)(26,30)(28,40)(29,31)(33,42)(34,35)(37,38);(9,10)(11,12)(13,17)(14,26)(15,29)(16,21)(18,22)(19,23)(20,27)(24,36)(25,32)(28,42)(30,38)(31,37)(33,41)(34,39)(35,40)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 590);