Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
| direct product | 3−1+2×C19⋊C3 |
| Fitting | C19×3−1+2 ⋊ C3 |
| Sylow | C19 ⋊ C3×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C19⋊C3 |
| commutator, socle, cosocle | C3×C19 | C33 |
| Fitting | C19×3−1+2 | C3 |
| prime radical | C32×C19⋊C3 | C3 |
| hypercenter | 3−1+2 | C19⋊C3 |
| hypocenter | C19 | C3×3−1+2 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ 3−1+2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 171 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×AΣL(1,𝔽27), C19⋊C3×#731, C19⋊C3×#733, … |
| maximal normal subgroup of | C19⋊C3×AΣL(1,𝔽27), C19⋊C3×#731, C19⋊C3×#733, … |
| maximal quotient of | C19⋊C3×C32⋊C9, C19⋊C3×C9⋊C9, #17987409, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 42);