General information, Order(G) = 64, Hall-Senior number = 21

Group #21: Cyclic(2) x Group(32)#17

Magma small group library number: 248

General information about the group

PC-Group relations:
g₁² = g₂	g₂² = g₆	g₄² = g₆
g₃^-1 g₄ g₃ = g₄ g₆

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

Orders of the Maximal Elementary Abelian Subgroups: [ 8, 8, 8 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32, 32, 32 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64, 64, 64 ]