Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22⋊Q8×A5 |
| unambiguous semidirect product | C22⋊(Q8×A5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, cosocle | C22 | C23×A5 |
| commutator, socle | C22×A5 | C23 |
| Fitting, hypercenter | C22⋊Q8 | A5 |
| prime radical | C23×A5 | C22 |
| hypocenter | A5 | C22⋊Q8 |
| LCS | G ▷ C22×A5 ▷ A5 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
752 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240520);