Group #22

Magma small group library number: 17

General information about the group

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

Center abelian of type: [ 8 ]

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

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

Order of the Frattini Subgroup: 8

Exponent of G: 16

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: 264 , 363 , 66 , 672 , 1332 , 1822 , 244 , 245 , 246 , 247 , 248 , 249

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

of order 64 and Hall-Senior numbers: 262 , 392 , 40 , 41