Group #45

Magma small group library number: 44

General information about the group

PC-Group relations:
g12 = g5	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, 4 ]

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16, 8 ]

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32, 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: 1118 , 1124 , 2423 , 2436 , 257 , 2582 , 2622 , 2642

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

of order 64 and Hall-Senior numbers: 1112 , 114 , 1152 , 116 , 118 , 1192 , 203 , 204 , 207 , 208 , 210 , 211 , 213 , 215 , 218 , 220 , 222 , 224 , 2262 , 227 , 229 , 2302 , 232 , 2332