Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊#4296 |
| unambiguous semidirect product | (C3×#4296)⋊C3 |
| Fitting | C32×C19 ⋊ C9 |
| Sylow | C19 ⋊ C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#4296 |
| commutator, socle | C3×C19 | C3×C9 |
| Fitting | C32×C19 | C9 |
| prime radical | C32×C19⋊C3 | C3 |
| cosocle | C3×C19⋊C3 | C32 |
| hypercenter | C32 | #4296 |
| hypocenter | C19 | C32⋊C9 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ C32 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 171 |
Polycyclic presentation:
3^4,19|a^3=d,b^a=bc,e^a=e^4,e^d=e^751 conjugacy classes — view the full character table.
| maximal subgroup of | #17987558, #17987559, #17987560, … |
| maximal normal subgroup of | #17987558, #17987559, #17987560, … |
| maximal quotient of | (C3×#4296)⋊C9, C32⋊#10587020, #17987557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 52);