Group #44

Magma small group library number: 43

General information about the group

PC-Group relations:
g42 = g5	g1-1 g3 g1 = g3 g4
g2-1 g3 g2 = g3 g5		g1-1 g4 g1 = g4 g5
g3-1 g4 g3 = 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: 4

Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4, 8 ]

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 16, 16 ]

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: 1108 , 1124 , 2416 , 2423 , 2562 , 257 , 2612 , 2632

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

of order 64 and Hall-Senior numbers: 1102 , 1132 , 114 , 116 , 1172 , 118 , 201 , 202 , 205 , 206 , 209 , 212 , 214 , 216 , 217 , 219 , 221 , 223 , 2252 , 227 , 2282 , 229 , 2312 , 232