Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×#90265 |
| Fitting | C3×C4×C7×Q8 ⋊ C2 |
| Hall | C3×C7 ⋊ #520 |
| Sylow | C7 ⋊ C3×#520 |
588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 672 |
A minimal faithful permutation representation — 4 generators on 22 points:
(1,2,3)(4,5,7,9,10,8,6)(11,13,14,12)(15,17,18,21)(16,20,19,22);(11,12,14,13)(16,19)(20,22);(15,16,18,19)(17,20,21,22);(5,6)(7,8)(9,10)(17,21)(20,22)282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 10205);