Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C5×H(3,𝔽3) ⋊ C3×C4 |
| Hall | C5×AΣL(1,𝔽27) ⋊ C4 |
| Sylow | AΣL(1,𝔽27) ⋊ Dic5 |
| Sylow | C5 ⋊ #66321 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2,3,2,3^2,5,3|a^2=c,d^a=d^2,e^a=e^2g,f^a=f^4,d^b=de,e^d=eg112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 42);