Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | Q8×Dic3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ C42×Q8 |
| Sylow | C5 ⋊ C4×Q8×Dic3 |
| Sylow | C3 ⋊ C4×Q8×AGL(1,𝔽5) |
1368 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 45335);