Finite Group DatabasebetaFinite Group Databasebeta| order | 522 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | D9×C29 |
| unambiguous semidirect product | C9⋊(C2×C29) |
| Fitting, Hall | C9×C29 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C29 |
| Frattini | C3 | D3×C29 |
| Fitting | C9×C29 | C2 |
| socle | C3×C29 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 261 |
174 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D29, C2×D9×C29, C29×D27, … |
| maximal normal subgroup of | D9×D29, C2×D9×C29, C3×D9×C29, … |
| maximal quotient of | C29×Dic9, C2×D9×C29, C29×D27, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(522, 1);