Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C81 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C19 ⋊ C81 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C9 | #4296 |
| commutator, hypocenter | C19 | C81 |
| Fitting | C9×C19 | C9 |
| socle, prime radical | C3×C19 | C27 |
| cosocle | #10587018 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C9 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 100 |
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^4,19|a^3=b,b^3=c,c^3=d,e^a=e^4,e^b=e^799 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13095335, (C19⋊C3)⋊C81, #17987582, … |
| maximal normal subgroup of | C3×#13095335, (C19⋊C3)⋊C81, #17987582, … |
| maximal quotient of | #17987549, C3×#13095335 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 50);