Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1376 |
| Sylow | C5 ⋊ #67658 |
| Sylow | C3 ⋊ #10598700 |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=cg,e^a=eg,h^a=h^2,i^a=i^2,i^d=i^4216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4423);