Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C28 |
| direct product | C3×#10619040 |
| Fitting | C3×C5×#564 ⋊ C2 |
| Hall | C3×C5 ⋊ #3531 |
| Sylow | C5 ⋊ C3×#3531 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C3 | C24×D5 |
| commutator, cosocle | C22×C5 | C25×C3 |
| Frattini | C22 | C24×C3×D5 |
| Fitting | C3×C5×#564 | C2 |
| socle | C22×C3×C5 | C25 |
| hypercenter | C3×#564 | D5 |
| hypocenter | C5 | C3×#3531 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C3 ◁ C3×#564 | |
1860 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 221302);