Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C8 · Schur multiplier (H2) = C1 |
| direct product | C7×SL(2,𝔽3)⋊C8 |
| unambiguous semidirect product | SL(2,𝔽3)⋊(C7×C8) |
| derived | SL(2,𝔽3) ⋊ C7×C8 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3,4,5,6,7)(8,9,10,12,11,13,14,15)(16,17,23,18,19,22,21,20);(17,20,23)(18,21,22)224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 822);