Finite Group DatabasebetaFinite Group Databasebeta| order | 522 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D29 |
| unambiguous semidirect product | C29⋊(C2×C32) |
| Fitting, socle, Hall | C32×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 261 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#1181, C3×C3⋊#1181, C3⋊(C3⋊#1181), … |
| maximal normal subgroup of | C32×#1181, C3×C3⋊#1181, C3⋊(C3⋊#1181), … |
| maximal quotient of | C32×Dic29, C2×C32×D29, C3×C9×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(522, 5);