Finite Group DatabasebetaFinite Group Databasebeta| order | 540 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C9×AGL(1,𝔽5) |
| Fitting, Hall | C3×C5×C9 ⋊ C4 |
| derived, Sylow | C5 ⋊ C3×C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C3×C4×C9 |
| Frattini | C3 | C32×AGL(1,𝔽5) |
| Fitting | C3×C5×C9 | C4 |
| socle | C32×C5 | C3×C4 |
| prime radical | C32×D5 | C2×C3 |
| cosocle | C3×D5 | C2×C32 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(540, 32);