Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C1 |
| direct product | M32×C13⋊C3 |
| unambiguous semidirect product | (C13×M32)⋊C3 |
| Fitting, Hall | C13×M32 ⋊ C3 |
| Sylow | C13 ⋊ C3×M32 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(18,19,21)(20,23,26)(22,25,24)(27,29,28);(2,10)(4,12)(6,14)(8,16)(17,18,20,19,22,26,23,27,29,21,24,28,25)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 133);