Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#89900 |
| Fitting | C2×C3×C7×M16 ⋊ C2 |
| Hall | C3×C7 ⋊ #436 |
| Sylow | C7 ⋊ C3×#436 |
244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 672 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3)(4,5,7,9,10,8,6)(15,16,17,20,18,19,21,22);(12,14)(16,19)(20,22);(5,6)(7,8)(9,10)(11,12)(13,14)(16,19)(20,22)264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4841);