Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#91571 |
| Hall | C3×C5 ⋊ C22×#121 |
| Sylow | C5 ⋊ C22×#939 |
| Sylow | C3 ⋊ C22×#4085 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D3×D5 |
| commutator, cosocle | C22×C3×C5 | C25 |
| Frattini | C22 | C23×D3×D5 |
| Fitting | C25×C3×C5 | C22 |
| socle | C24×C3×C5 | C23 |
| hypercenter | C25 | D3×D5 |
| hypocenter | C3×C5 | C22×#121 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C24 ◁ C25 | |
5056 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 205095);