Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×D4×D5×A4 |
| unambiguous semidirect product | (C23×D4×D5)⋊C3 |
| Fitting | C23×C5×D4 ⋊ C2×C3 |
| Hall | C23×D4×D5 ⋊ C3 |
| Sylow | C5 ⋊ C22×D4×A4 |
4304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×A4×S4 |
| maximal quotient of | D5×#3585⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240345);