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×C4×C3⋊#674 |
| derived, Hall | C3×C5 ⋊ C2×C4×C16 |
| Sylow | C5 ⋊ C2×C4×C3⋊C16 |
| Sylow | C3 ⋊ C2×C4×#674 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1920 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 38213);