Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C16×ΓL(1,𝔽16) |
| Fitting | C2×C3×C5×C16 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C2×C4×C16 |
| Sylow | C5 ⋊ C2×Dic3×C16 |
| Sylow | C3 ⋊ C2×C16×AGL(1,𝔽5) |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38211);