General information, Order(G) = 64, Hall-Senior number = 152

Group #152

Magma small group library number: 81

General information about the group

PC-Group relations:
g₁² = g₄ g₆	g₂² = g₄	g₃² = g₆
g₁^-1 g₂ g₁ = g₂ g₄		g₁^-1 g₃ g₁ = g₃ g₅
g₂^-1 g₃ g₂ = g₃ g₆

Center abelian of type: [ 2, 2, 2 ]
Orders of the terms of the Lower Central Series: [ 64, 8, 1 ]
Orders of the terms of the Upper Central Series: [ 1, 8, 64 ]
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: [ 64 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64 ]