Finite Group DatabasebetaFinite Group Databasebeta| order | 1521 |
| isoclinism | isoclinic class of C169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C169⋊C9 |
| derived, Sylow | C169 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C169⋊C3 |
| commutator, hypocenter | C169 | C9 |
| Frattini, socle, prime radical | C3×C13 | C13⋊C3 |
| Fitting, cosocle | C3×C169 | C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C3 | |
9 conjugacy classes of subgroups.
| minimal degree | μ(G) = 178 |
| transitive degree | μt(G) = 1521 |
Polycyclic presentation:
3^2,13^2|a^3=b,c^13=d,c^a=c^9d,d^a=d^9177 conjugacy classes — view the full character table.
| maximal subgroup of | D169⋊C9, C2×C169⋊C9, C11×C169⋊C9, … |
| maximal normal subgroup of | D169⋊C9, C2×C169⋊C9, C11×C169⋊C9, … |
| maximal quotient of | C2×C169⋊C9, C11×C169⋊C9, C17×C169⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1521, 1);