Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of #13108177 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, Hall | C5×C32⋊C9 ⋊ C4 |
| derived | C3×C5×C9 ⋊ C3×C4 |
| Sylow | C32⋊C9 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #66316 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C3×C5×C9 | C3×C4 |
| Frattini | C32 | C3×ΓL(1,𝔽16) |
| Fitting | C5×C32⋊C9 | C4 |
| socle | C32×C5 | C3×Dic3 |
| prime radical | C33×D5 | D3 |
| cosocle | C3×C9×D5 | C2×C3 |
| LCS | G ▷ C3×C5×C9 | |
| UCS | C1 | |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 135 |
Polycyclic presentation:
2,3,2,3^2,5,3|a^2=c,d^3=g,d^a=d^2g^2,e^a=e^2,f^a=f^2,g^a=g^2,d^b=de,f^c=f^475 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#4169, #72247379, #72247383, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#4169, #72247379, #72247383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 83);