Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#88119 |
| Fitting | C23×C3×C13 ⋊ C4 |
| Hall | C3×C13 ⋊ #99 |
| Sylow | C13 ⋊ C3×#99 |
104 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)(4,5,8,11,15,9,13,14,6,10,16,12,7)(17,19)(18,21)(20,24)(22,23);(5,6,7,9)(8,11,12,16)(10,14,15,13)(17,18)(19,23,24,21)(20,22)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 468);