Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of A4⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×A4⋊Dic13 |
| unambiguous semidirect product | (C2×A4)⋊Dic13 |
| derived | A4×C13 ⋊ C2×C4 |
| Sylow | C13 ⋊ C2×SL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | A4⋊D13 |
| commutator, hypocenter | A4×C13 | C2×C4 |
| Frattini | C2 | C2×A4⋊D13 |
| Fitting, socle | C24×C13 | D3 |
| prime radical | C22×A4×C13 | C2 |
| cosocle | C2×A4×C13 | C22 |
| LCS | G ▷ A4×C13 | |
| UCS | C1 ◁ C22 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1240);