Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | #99×ΓL(1,𝔽16) |
| Fitting | C3×C5×#99 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×#99 |
| Sylow | C5 ⋊ Dic3×#99 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#99 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽16)×B(4,𝔽2), D3×AGL(1,𝔽5)×#99, #72229650 |
| maximal normal subgroup of | ΓL(1,𝔽16)×B(4,𝔽2), D3×AGL(1,𝔽5)×#99, #72229650 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21079);