Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #6104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#88048 |
| Hall | C3×C13 ⋊ #106 |
| Sylow | C13 ⋊ C3×#106 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1248 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3)(4,5,7,9,11,13,15,16,14,12,10,8,6)(17,18,19,20)(22,25)(23,27)(26,28);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(21,22,23,25,24,26,27,28)222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 150);