Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×C42×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2×C42 | A5 |
| commutator, hypocenter | A5 | C2×C42 |
| Frattini, cosocle | C22 | C23×A5 |
| socle, prime radical | C23×A5 | C22 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C2×C42 | |
1178 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240481);