Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C3×#10608900 |
| Fitting | C3×C5×#395 ⋊ C2 |
| Hall | C3×C5 ⋊ #2388 |
| Sylow | C5 ⋊ C3×#2388 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C3 | C23×D5 |
| commutator, cosocle | C23×C5 | C24×C3 |
| Frattini | C23 | C23×C3×D5 |
| Fitting | C3×C5×#395 | C2 |
| socle | C23×C3×C5 | C24 |
| hypercenter | C3×#395 | D5 |
| hypocenter | C5 | C3×#2388 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23×C3 ◁ C3×#395 | |
1888 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 57321);