Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#88165 |
| Fitting | C3×C13×D8 ⋊ C2 |
| Hall | C3×C13 ⋊ AGL(1,ℤ/8) |
| Sylow | C13 ⋊ C3×AGL(1,ℤ/8) |
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 312 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,9,11,13,15,16,14,12,10,8,6)(17,18)(19,24)(20,21)(22,23);(18,22)(19,23)(21,24);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(18,21)(22,24)159 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 913);