Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×AGL(1,𝔽5)×#99 |
| Fitting | C3×C5×#99 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×#99 |
| Sylow | C5 ⋊ C3×C4×#99 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×B(4,𝔽2), D3×AGL(1,𝔽5)×#99, AGL(1,𝔽5)×#4741 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×B(4,𝔽2), D3×AGL(1,𝔽5)×#99, AGL(1,𝔽5)×#4741 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21078);