Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C3×C4 |
| direct product | C8×C3⋊ΓL(1,𝔽16) |
| Fitting | C32×C5×C8 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C8×C3⋊Dic3 |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2610);