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 | C4×C3⋊(C3⋊#170) |
| derived, Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C4×#170 |
| Sylow | C5 ⋊ C4×C3⋊(C3⋊C8) |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2619);