Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C42 |
| direct product | ΓL(1,𝔽8)×#376 |
| Fitting, Hall | C7×#376 ⋊ C3 |
| Sylow | C7 ⋊ C3×#376 |
356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3,4)(5,7,6)(8,9,10,11)(16,17)(18,21)(19,20)(22,23);(1,2,3,5,4,6,7)(12,13,14,15)(17,20)(21,23);(16,18,19,22)(17,21,20,23)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4196);