Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C2×D4×#1220 |
| Fitting | C23×C3×C5×D4 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×D42 |
| Sylow | C5 ⋊ C2×D4×#67 |
| Sylow | C3 ⋊ C2×D4×C22⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D15 |
| commutator, cosocle | C22×C3×C5 | C25 |
| Frattini | C22 | C24×D15 |
| Fitting | C23×C3×C5×D4 | C2 |
| socle | C23×C3×C5 | C24 |
| hypercenter | C23×D4 | D15 |
| hypocenter | C3×C5 | C2×D42 |
| LCS | G ▷ C22×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
5072 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 208106);