Group #32

Magma small group library number: 15

General information about the group

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

Center abelian of type: [ 4 ]

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

Orders of the terms of the Upper Central Series: [ 1, 4, 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: 524 , 58 , 1214 , 122 , 142 , 1432 , 246 , 247 , 249 , 256 , 257 , 258

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

of order 64 and Hall-Senior numbers: 522 , 612 , 64 , 65