Abelian group, Order(G) = 32, Hall-Senior number = 4

Group #4: Abelian(8,2,2)

Magma small group library number: 36

Cohomology ring P = H^*(G) is a quotient of
Polynomial ring in variables: z , y , x , w
in degrees: 1 , 1 , 1 , 2
The ideal of relations is generated by: z²

SUPERGROUPS AND SUPERQUOTIENTS
The subindices indicate multiplicities.
This group is a maximal subgroup of the non-abelian groups
of order 64 and Hall-Senior numbers: 17₂ , 21₃ , 23₂ , 24₂ , 25₂ , 26 , 32 , 34₂ , 37₂ , 40 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 52 , 53 , 54 , 59 , 61 , 96 , 97 , 99 , 195 , 196 , 197
This group is a maximal quotient of the non-abelian groups
of order 64 and Hall-Senior numbers: 24 , 25 , 26 , 33 , 34 , 35 , 36