Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#88207 |
| Fitting | C24×C3×C13 ⋊ C2 |
| Hall | C3×C13 ⋊ #120 |
| Sylow | C13 ⋊ C3×#120 |
260 conjugacy classes of subgroups.
| 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)(18,20);(22,24);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 955);