Finite Group DatabasebetaFinite Group Databasebeta| order | 1620 |
| isoclinism | isoclinic class of C5⋊(D27⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C27⋊C3)⋊Dic5 |
| unambiguous semidirect product | Dic135⋊C3 |
| derived | C5×C27 ⋊ C3×C4 |
| Hall | C5×C27⋊C3 ⋊ C4 |
| Sylow | C27⋊C3 ⋊ Dic5 |
| Sylow | C5 ⋊ (C27⋊C3)⋊C4 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 540 |
Polycyclic presentation:
2,3,2,3,5,3^2|a^2=c,d^3=f,f^3=g,d^a=d^2f^2g^2,e^a=e^4,f^a=f^2g^2,g^a=g^2,d^b=dg174 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1620, 41);