General information, Order(G) = 64, Hall-Senior number = 18

Group #18: Abelian(4,2) x Dihedral(8)

Magma small group library number: 196

General information about the group

PC-Group relations:
g₁² = g₃	g₅² = g₆	g₂^-1 g₅ g₂ = g₅ g₆

Center abelian of type: [ 2, 2, 4 ]
Orders of the terms of the Lower Central Series: [ 64, 2, 1 ]
Orders of the terms of the Upper Central Series: [ 1, 16, 64 ]
Order of the Frattini Subgroup: 4
Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 16, 16 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32, 32 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64, 64 ]