Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C3×C5 ⋊ Q8×M16 |
| Sylow | C5 ⋊ Q8×#208 |
| Sylow | C3 ⋊ #10617193 |
776 conjugacy classes of subgroups.
| transitive degree | μt(G) = 960 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,h^a=h^2,i^a=i^3,d^c=dg,h^c=h^2,i^c=i^2,i^d=i^4,i^f=i^4150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 144523);