Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C13 · Schur multiplier (H2) = C24 |
| direct product | C23×A4×C13 |
| Fitting, socle, Hall | C25×C13 ⋊ C3 |
| derived | C22 ⋊ C23×C3×C13 |
| Sylow | C25 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C13 | A4 |
| commutator, cosocle, hypocenter | C22 | C23×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C25×C13 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C23×C13 | |
356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 312 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1453);