Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | D8×S5 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×S5 |
| commutator, cosocle | C4×A5 | C23 |
| Frattini | C4 | C22×S5 |
| Fitting, hypercenter | D8 | S5 |
| socle | C2×A5 | C2×D4 |
| hypocenter | A5 | C2×D8 |
| LCS | G ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
573 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
49 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240560);