Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C3×C5×C22⋊C4 ⋊ C22 |
| Hall | C3×C5 ⋊ #2308 |
| Sylow | C5 ⋊ #74874 |
| Sylow | C3 ⋊ #10606605 |
2320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=g,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^2,h^d=h^2,i^d=i^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 48096);