Finite Group DatabasebetaFinite Group Databasebeta| order | 522 |
| isoclinism | isoclinic class of C3⋊D87 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D87 |
| unambiguous semidirect product | C29⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C29 ⋊ C2 |
| Sylow | C29 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C29 | C2 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 261 |
Polycyclic presentation:
2,3^2,29|b^a=b^2,c^a=c^2,d^a=d^28132 conjugacy classes — view the full character table.
| maximal subgroup of | #11760329, C3⋊D3×D29, D3×D87, … |
| maximal normal subgroup of | #11760329, C3⋊D3×D29, D3×D87, … |
| maximal quotient of | C3⋊Dic87, C2×C3⋊D87, C3⋊D261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(522, 9);