General information, Order(G) = 64, Hall-Senior number = 22

Group #22: Cyclic(2) x Group(32)#18

Magma small group library number: 56

General information about the group

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

Center abelian of type: [ 2, 2, 2, 2 ]
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: 8
Exponent of G: 4

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