General information, Order(G) = 64, Hall-Senior number = 100

Group #100

Magma small group library number: 117

General information about the group

PC-Group relations:
g₁² = g₃	g₃² = g₅	g₄² = g₆
g₁^-1 g₂ g₁ = g₂ g₅		g₂^-1 g₄ g₂ = g₄ g₆

Center abelian of type: [ 2, 4 ]
Orders of the terms of the Lower Central Series: [ 64, 4, 1 ]
Orders of the terms of the Upper Central Series: [ 1, 8, 64 ]
Order of the Frattini Subgroup: 8
Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 8, 8 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16, 16 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64, 64 ]