Finite Group DatabasebetaFinite Group Databasebeta| order | 1350 |
| isoclinism | isoclinic class of #90646⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #90646⋊C3 |
| derived | C52⋊C9 ⋊ C2×C3 |
| Hall | #10621712 ⋊ C2 |
| Sylow | C52 ⋊ AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊C9 | C2×C3 |
| Frattini | C3 | C3×#3874 |
| Fitting | C32×C52 | D3 |
| socle | C3×C52 | C3×D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2,3^3,5^2|c^3=d,c^a=c^2d^2,d^a=d^2,e^a=ef^2,f^a=f^4,c^b=cd,e^c=e^3f^3,f^c=e^4f64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1350, 42);