Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C3×C5 ⋊ #2943 |
| Sylow | C5 ⋊ #79828 |
| Sylow | C3 ⋊ #10611559 |
984 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=f,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^2,e^b=eg,h^b=h^2,i^b=i^4,h^c=h^2,h^d=h^2,i^d=i^4138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 142329);