Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | Q32×A5 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×A5 |
| commutator | C8×A5 | C22 |
| Frattini, cosocle | C8 | C22×A5 |
| Fitting, hypercenter | Q32 | A5 |
| socle, prime radical | C2×A5 | D8 |
| hypocenter | A5 | Q32 |
| LCS | G ▷ C8×A5 ▷ C4×A5 ▷ C2×A5 ▷ A5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32 | |
182 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
55 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240478);