Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#5403 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 71 points:
(1,2,3,4,5,6,7)(8,23,57,33,31,53,11,48,30,10,46,71,14,52,56,22,12,51,21,58,32,25,27,70)(9,34,65,45,41,63,16,43,40,15,54,69,19,62,64,20,17,61,26,68,42,36,37,67)(13,24,47,59,29,50,28,49)(18,35,55,66,39,60,38,44);(8,9,14,19)(10,20,25,45)(11,26,21,16)(12,18,31,39)(13,17,29,41)(15,33,36,22)(23,44,52,66)(24,43,50,68)(27,55,46,38)(28,54,47,37)(30,42,32,40)(34,59,62,49)(35,58,60,48)(51,69,53,67)(56,64,57,65)(61,70,63,71)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6412);