Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C2×C4×A4×C13 |
| unambiguous semidirect product | (C23×C4)⋊(C3×C13) |
| Fitting, Hall | C23×C4×C13 ⋊ C3 |
| derived | C22 ⋊ C2×C3×C4×C13 |
| Sylow | C23×C4 ⋊ C3×C13 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1364);