Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of 3−1+2⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C9⋊C9)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C9⋊AGL(1,𝔽5))⋊C9 |
| Fitting, Hall | C5×C9⋊C9 ⋊ C4 |
| derived | C5×C9 ⋊ C4×C9 |
| Sylow | C9⋊C9 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic9⋊C9 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 90 |
Polycyclic presentation:
2,3,2,3^2,5,3|a^2=c,b^3=d,e^3=g,e^a=e^2g^2,f^a=f^2,g^a=g^2,e^b=eg^2,f^c=f^493 conjugacy classes — view the full character table.
| maximal subgroup of | #72222360, AGL(1,𝔽5)×D9⋊C9, #72247132 |
| maximal normal subgroup of | #72222360, AGL(1,𝔽5)×D9⋊C9 |
| maximal quotient of | #72247132 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 84);