Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C3⋊#674 |
| unambiguous semidirect product | (C2×C3)⋊(C3×#674) |
| derived | C3×C5 ⋊ C2×C3×C16 |
| Hall | C32×C5 ⋊ C2×C16 |
| Sylow | C32 ⋊ C2×#674 |
| Sylow | C5 ⋊ C2×C3×C3⋊C16 |
134 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2591);