Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C32 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#3928 |
| unambiguous semidirect product | C3⋊(C3×#3928) |
| derived | C3×C5 ⋊ C3×C32 |
| Hall | C32×C5 ⋊ C32 |
| Sylow | C32 ⋊ #3928 |
| Sylow | C5 ⋊ C3×C3⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C3×C32 |
| Frattini | C8 | C3×ΓL(1,𝔽16) |
| Fitting | C32×C5×C8 | C4 |
| socle, prime radical | C2×C32×C5 | C16 |
| cosocle | C3×#672 | C2×C3 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C8 | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| 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, 944);