Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C22⋊(A5⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×S5 |
| commutator | C2×A5 | C22×C4 |
| Frattini | C22 | C22×S5 |
| Fitting, hypercenter | C24 | S5 |
| socle | C23×A5 | C22 |
| prime radical | C24×A5 | C2 |
| cosocle | C22×A5 | C23 |
| hypocenter | A5 | C2×C22⋊C4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C23 ◁ C24 | |
1641 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 1641 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240482);