Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C8×ΓL(1,𝔽16) |
| Fitting | C22×C3×C5×C8 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C22×C4×C8 |
| Sylow | C5 ⋊ C22×C8×Dic3 |
| Sylow | C3 ⋊ C22×C8×AGL(1,𝔽5) |
1520 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, 136865);