General information, Order(G) = 64, Hall-Senior number = 63

Group #63

Magma small group library number: 7

General information about the group

PC-Group relations:
g₁² = g₃ g₅ g₆	g₂² = g₃	g₃² = g₄	g₅² = g₆
g₁^-1 g₂ g₁ = g₂ g₅		g₂^-1 g₅ g₂ = 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: 16
Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 64 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64 ]