Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C3×C5×C22⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×#99 |
| Sylow | C5 ⋊ C4×#834 |
| Sylow | C3 ⋊ #10604216 |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=e,b^a=bd,f^a=fg,i^a=i^4,d^b=dg,h^b=h^2,i^b=i^2,i^c=i^4,i^f=i^4144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21077);