Group #48

Magma small group library number: 8

General information about the group

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

Center abelian of type: [ 2 ]

Orders of the terms of the Lower Central Series: [ 32, 4, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 2, 8, 32 ]

Order of the Frattini Subgroup: 8

Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32 ]

SUPERGROUPS AND SUPERQUOTIENTS

The subindices indicate multiplicities.

This group is a maximal subgroup of the non-abelian groups

of order 64 and Hall-Senior numbers: 1254 , 1272 , 2542 , 2552 , 257 , 2582 , 263 , 264

This group is a maximal quotient of the non-abelian groups

of order 64 and Hall-Senior numbers: 1252 , 129 , 132 , 235 , 240