Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C19⋊C3)⋊C27 |
| derived, Sylow | C19 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #4296 |
| commutator, hypocenter | C19 | C3×C27 |
| Frattini | C3 | C3×#4296 |
| Fitting | C9×C19 | C9 |
| socle | C3×C19 | C3×C9 |
| prime radical | C3×C19⋊C3 | C9 |
| cosocle | #4294 | C32 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C9 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^4,19|a^3=c,c^3=d,e^a=e^4,e^b=e^11,e^c=e^799 conjugacy classes — view the full character table.
| maximal subgroup of | C27×#4296, #17987553, #17987554, … |
| maximal normal subgroup of | C27×#4296, #17987553, #17987554, … |
| maximal quotient of | C9×#10587020, #17987557, #17987572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 56);