Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊(C3⋊#674) |
| unambiguous semidirect product | (C2×C3)⋊(C3⋊#674) |
| derived, Hall | C32×C5 ⋊ C2×C16 |
| Sylow | C32 ⋊ C2×#674 |
| Sylow | C5 ⋊ C2×C3⋊(C3⋊C16) |
168 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, 2616);