Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C29 |
| direct product | C5×D4×#237 |
| Fitting | C3×C5×D42 ⋊ C2 |
| Hall | C3×C5 ⋊ D4×#41 |
| Sylow | C3 ⋊ C5×D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C24×D3 |
| commutator, cosocle | C22×C3 | C25×C5 |
| Frattini | C22 | C24×C5×D3 |
| Fitting | C3×C5×D42 | C2 |
| socle | C22×C3×C5 | C25 |
| hypercenter | C5×D42 | D3 |
| hypocenter | C3 | C5×D4×#41 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22×C5 ◁ C5×D42 | |
3296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 208728);