Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C19 ⋊ C27⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#4296 |
| commutator, socle | C3×C19 | C3×C9 |
| Fitting, prime radical | C32×C19 | C9 |
| cosocle | #4294 | C32 |
| hypercenter | C32 | #4296 |
| hypocenter | C19 | C27⋊C3 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C3 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^4,19|a^3=c,c^3=d,b^a=bd,e^a=e^4,e^c=e^751 conjugacy classes — view the full character table.
| maximal subgroup of | #17987561, #17987562, #17987563, … |
| maximal normal subgroup of | #17987561, #17987562, #17987563, … |
| maximal quotient of | #17987555, C32⋊#10587020, #17987572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 57);