Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | ΓL(1,𝔽8)×#384 |
| Fitting, Hall | C7×#384 ⋊ C3 |
| Sylow | C7 ⋊ C3×#384 |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3,4)(5,7,6)(9,11)(13,14)(16,17,18,19);(1,2,3,5,4,6,7)(12,13,15,14);(8,9,10,11)(12,14,15,13)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4204);