Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#5398 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 336 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5,6,7)(8,9,11)(12,14,21,25,16,23,15,22)(13,17,24,27,19,26,18,20);(9,10)(12,13,16,19)(14,20,23,27)(15,24,21,18)(17,25,26,22)154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6407);