Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of D9⋊(C52⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | D9⋊(C52⋊C3) |
| Fitting, derived | C52×C9 ⋊ C2×C3 |
| Hall | C9⋊(C52⋊C3) ⋊ C2 |
| Sylow | C52 ⋊ AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9 | C2×C3 |
| Frattini | C3 | D3×C52⋊C3 |
| socle | C3×C52 | C3×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
Polycyclic presentation:
2,3^2,5^2,3|c^3=f,c^a=c^2f^2,f^a=f^2,c^b=cf^2,d^b=d^3e^2,e^b=de58 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 53);