Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#5213 |
| Fitting | C23×C3×C4×C7 ⋊ C2 |
| Hall | C3×C7 ⋊ #386 |
| Sylow | C3 ⋊ C7×#386 |
572 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 672 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2,3,4,5,6,7)(8,9,10)(11,12,13,14)(20,22);(16,18);(9,10)(15,16)(17,18)(19,20)(21,22)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5537);