Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×C5×C4⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #1477 |
| Sylow | C5 ⋊ #70425 |
| Sylow | C3 ⋊ #10601218 |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cf,d^b=df,h^b=h^2,i^b=i^4324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 7320);