Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×D4×A5 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×A5 |
| commutator | C2×A5 | C22×C4 |
| Frattini, cosocle | C22 | C23×A5 |
| Fitting, hypercenter | C4×D4 | A5 |
| socle | C22×A5 | C23 |
| prime radical | C2×D4×A5 | C2 |
| hypocenter | A5 | C4×D4 |
| LCS | G ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
1004 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240500);