Finite Group DatabasebetaFinite Group Databasebeta| order | 10539 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1171 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1171 | C9 |
| prime radical, cosocle | C1171⋊C3 | C3 |
| LCS | G ▷ C1171 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
3^2,1171|a^3=b,c^a=c^656,c^b=c^420139 conjugacy classes — view the full character table.
| maximal subgroup of | #24902008⋊C2, C2×#24902008, C3×#24902008 |
| maximal normal subgroup of | #24902008⋊C2, C2×#24902008, C3×#24902008 |
| maximal quotient of | C2×#24902008, #44539239, C3×#24902008 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10539, 3);