General information, Order(G) = 64, Hall-Senior number = 37

Group #37

Magma small group library number: 17

General information about the group

PC-Group relations:
g₁² = g₃	g₂² = g₄	g₃² = g₅	g₄² = g₅
g₁^-1 g₂ g₁ = g₂ g₆

Center abelian of type: [ 2, 2, 4 ]
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: 16
Exponent of G: 8

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