Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#88063 |
| Fitting | C3×C13×M16 ⋊ C2 |
| Hall | C3×C13 ⋊ #100 |
| Sylow | C13 ⋊ C3×#100 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 312 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,7,9,11,13,15,16,14,12,10,8,6)(17,18,19,22,20,21,23,24);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(18,21)(19,23)213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 165);