General information, Order(G) = 64, Hall-Senior number = 51

Group #51: Cyclic(2) x Group(32)#31

Magma small group library number: 101

General information about the group

PC-Group relations:
g₁² = g₃	g₂² = g₆	g₃² = g₆	g₅² = g₆
g₁^-1 g₂ g₁ = g₂ g₆		g₁^-1 g₄ g₁ = g₄ g₅
g₂^-1 g₄ g₂ = g₄ g₆		g₁^-1 g₅ g₁ = g₅ g₆
g₄^-1 g₅ g₄ = g₅ g₆

Center abelian of type: [ 2, 4 ]
Orders of the terms of the Lower Central Series: [ 64, 4, 2, 1 ]
Orders of the terms of the Upper Central Series: [ 1, 8, 16, 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: [ 32, 16 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64, 32 ]