Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×#67⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C2×#67⋊C4) |
| Fitting | C24×C3×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C22×C4×D4 |
| Sylow | C5 ⋊ C22×#67⋊C4 |
| Sylow | C3 ⋊ C22×D4×AGL(1,𝔽5) |
5056 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 204531);