General information, Order(G) = 32, Hall-Senior number = 11

Group #11: Cyclic(2) x Group(16)#9

Magma small group library number: 22

General information about the group

PC-Group relations:
g₁² = g₂	g₁^-1 g₄ g₁ = g₄ 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: 4
Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 16 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16 ]
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: 15₁₂ , 18₂ , 20₂ , 28₂ , 68₃ , 71₂ , 72₂ , 73₃ , 74₄ , 76₃ , 81₆ , 83₂ , 84₃ , 85₄ , 86₂ , 89₂ , 91₃ , 106₄ , 123₂ , 128₃ , 131 , 144₃ , 146₄ , 147₃ , 148₃ , 150₃ , 151₃ , 157₂ , 163₂ , 169 , 173₃ , 175
This group is a maximal quotient of the non-abelian groups
of order 64 and Hall-Senior numbers: 15₁₂ , 22₃ , 24 , 28 , 47 , 48 , 51 , 53 , 81₃ , 83 , 84 , 85 , 87 , 89 , 94 , 96 , 113 , 114 , 115 , 120 , 123 , 124 , 125 , 126 , 127