Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q8×#41 |
| Sylow | C5 ⋊ #41×Dic6 |
| Sylow | C3 ⋊ #10618916 |
2136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,i^b=i^4,h^c=h^2,i^d=i^4,i^e=i^4180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 210391);