Group #25

Magma small group library number: 41

General information about the group

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

Center abelian of type: [ 2, 2 ]

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: 4

Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]

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

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: 4512 , 46 , 57 , 1112 , 119 , 135 , 1362 , 139 , 1924 , 197 , 198 , 2042 , 2112 , 218 , 220 , 2262 , 230 , 2433 , 245 , 249 , 258

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

of order 64 and Hall-Senior numbers: 456 , 48 , 49 , 57 , 190 , 1922 , 194 , 197 , 204 , 211 , 212 , 216