General information, Order(G) = 64, Hall-Senior number = 76

Group #76: Cyclic(2) x Group(32)#41

Magma small group library number: 209

General information about the group

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

Center abelian of type: [ 2, 2, 2 ]
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: 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: [ 64 ]