Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of A4⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C22×A4⋊D13 |
| Fitting, socle | C24×C13 ⋊ D3 |
| derived | A4×C13 ⋊ C23 |
| Sylow | C13 ⋊ C22×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | A4⋊D13 |
| commutator, cosocle, hypocenter | A4×C13 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C24×C13 | D3 |
| LCS | G ▷ A4×C13 | |
| UCS | C1 ◁ C22 | |
262 conjugacy classes of subgroups.
| transitive degree | μt(G) = 156 |
116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1441);