Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8×C13 · Schur multiplier (H2) = C2 |
| direct product | C8×A4×C13 |
| unambiguous semidirect product | (C22×C8)⋊(C3×C13) |
| Fitting, Hall | C22×C8×C13 ⋊ C3 |
| derived | C22 ⋊ C3×C8×C13 |
| Sylow | C22×C8 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C13 | A4 |
| commutator, hypocenter | C22 | C3×C8×C13 |
| Frattini | C4 | C2×A4×C13 |
| Fitting | C22×C8×C13 | C3 |
| socle | C23×C13 | C3×C4 |
| prime radical | C2×A4×C13 | C4 |
| cosocle | C22×C4 | C2×C3×C13 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C8×C13 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| 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, 860);