Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C23×C3⋊ΓL(1,𝔽16) |
| unambiguous semidirect product | D5⋊(C22×C3⋊Dic3) |
| Fitting, socle | C23×C32×C5 ⋊ C4 |
| derived, Hall | C32×C5 ⋊ C23×C4 |
| Sylow | C32 ⋊ C23×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C23×C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32×C5 | C4 |
| prime radical | C23×C32×D5 | C2 |
| cosocle | C32×D5 | C24 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
1416 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, 5942);