Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of #6104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#88049 |
| Fitting | C3×C13×C4⋊C4 ⋊ C2 |
| Hall | C3×C13 ⋊ #102 |
| Sylow | C13 ⋊ C3×#102 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 624 |
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)(23,28)(26,27);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(21,22)(23,25)(24,27)(26,28)222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 151);