Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C19 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C19⋊C3 |
| commutator | C3×C19 | C3×C9 |
| Fitting | C3×C9×C19 | C3 |
| socle, prime radical, cosocle | C32×C19 | C32 |
| hypercenter | C3×C9 | C19⋊C3 |
| hypocenter | C19 | C9⋊C9 |
| LCS | G ▷ C3×C19 ▷ C19 | |
| UCS | C1 ◁ C32 ◁ C3×C9 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^4,19|a^3=d,b^3=c,b^a=bc,e^a=e^11195 conjugacy classes — view the full character table.
| maximal subgroup of | #17987360, #17987361, #17987378, … |
| maximal normal subgroup of | #17987360, #17987361, #17987378, … |
| maximal quotient of | #17987308, #17987357, #17987360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 22);