Finite Group DatabasebetaFinite Group Databasebeta| order | 1521 |
| isoclinism | isoclinic class of C169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C169⋊C3 |
| unambiguous semidirect product | C169⋊C32 |
| unambiguous semidirect product | (C3×C169)⋊C3 |
| Fitting | C3×C169 ⋊ C3 |
| derived, Sylow | C169 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C32 |
| Frattini | C13 | C3×C13⋊C3 |
| Fitting | C3×C169 | C3 |
| socle | C3×C13 | C13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 507 |
177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D169⋊C3, D3×C169⋊C3, C3⋊(D169⋊C3), … |
| maximal normal subgroup of | C3×D169⋊C3, D3×C169⋊C3, C3⋊(D169⋊C3), … |
| maximal quotient of | C2×C3×C169⋊C3, C3×C11×C169⋊C3, C3×C17×C169⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1521, 3);