Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #1768 |
| Sylow | C5 ⋊ #69436 |
| Sylow | C3 ⋊ #10603778 |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1920 |
Polycyclic presentation:
2^7,3,5|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,c^a=cg,h^b=h^2,i^b=i^2,i^f=i^4156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21888);