General information, Order(G) = 64, Hall-Senior number = 58

Group #58

Magma small group library number: 124

General information about the group

PC-Group relations:
g₁² = g₃	g₃² = g₆	g₄² = g₅	g₅² = g₆
g₂^-1 g₄ g₂ = g₄ g₅		g₂^-1 g₅ g₂ = g₅ g₆

Center abelian of type: [ 8 ]
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: [ 4, 4, 4 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32, 16, 16 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64, 32, 32 ]