Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊C4×C13⋊C3 |
| unambiguous semidirect product | (C2×C13×C22⋊C4)⋊C3 |
| Fitting, Hall | C2×C13×C22⋊C4 ⋊ C3 |
| Sylow | C13 ⋊ C2×C3×C22⋊C4 |
264 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(12,13,15)(14,17,20)(16,19,18)(21,23,22);(3,4,6,8)(5,7,9,10)(11,12,14,13,16,20,17,21,23,15,18,22,19);(4,7)(8,10)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 832);