General information, Order(G) = 32, Hall-Senior number = 18

Group #18

Magma small group library number: 2

General information about the group

PC-Group relations:
g₁² = g₃	g₂² = g₄	g₁^-1 g₂ g₁ = g₂ g₅

Center abelian of type: [ 2, 2, 2 ]
Orders of the terms of the Lower Central Series: [ 32, 2, 1 ]
Orders of the terms of the Upper Central Series: [ 1, 8, 32 ]
Order of the Frattini Subgroup: 8
Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 8 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32 ]

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: 22₄ , 28₂ , 29₂ , 30₄ , 83₂ , 84₂ , 86₂ , 87₄ , 88₂ , 89₄ , 90₄ , 91₂ , 92₄ , 93₆ , 144 , 145₃ , 146 , 147₃ , 148 , 149₃ , 150 , 151₃ , 152₅ , 153₇ , 237 , 238
This group is a maximal quotient of the non-abelian groups
of order 64 and Hall-Senior numbers: 22₈ , 37 , 59 , 60 , 61 , 128 , 129 , 130 , 180 , 181