Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1277 |
| Sylow | C5 ⋊ #67654 |
| Sylow | C3 ⋊ #10598771 |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=d,b^2=e,c^2=f,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=ef,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, 2451);