Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C5 ⋊ Q32 |
| Sylow | C32 ⋊ #3961 |
| Sylow | C5 ⋊ #63736 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^5,3^2,5|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=f^2g,h^a=h^4,c^b=cd,d^b=de,f^b=f^2g^2,f^c=f^2,g^c=g^263 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1906);