Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C5×Q8⋊C9 ⋊ C4 |
| Sylow | C5 ⋊ #63422 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^2,3,5,3,2^3|a^2=b,b^2=h,c^3=e,f^2=h,g^2=h,c^a=c^2e^2,d^a=d^2,e^a=e^2,f^a=fg,g^a=gh,d^b=d^4,f^c=g,g^c=fgh,g^f=gh51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1457);