Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C5 · Schur multiplier (H2) = C211 |
| direct product | C25×C5×A4 |
| Fitting, socle, Hall | C27×C5 ⋊ C3 |
| derived | C22 ⋊ C25×C3×C5 |
| Sylow | C27 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C5 | A4 |
| commutator, cosocle, hypocenter | C22 | C25×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C27×C5 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C25×C5 | |
21968 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
640 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237189);