Group #35

Magma small group library number: 35

General information about the group

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

Center abelian of type: [ 2, 2 ]

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

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

Order of the Frattini Subgroup: 4

Exponent of G: 4

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: 708 , 78 , 792 , 1553 , 1569 , 160 , 161 , 1623 , 166 , 168 , 1722 , 1744 , 178 , 179 , 1862 , 189 , 1902 , 1912 , 1922 , 193 , 1942 , 207 , 208 , 209 , 210 , 211 , 212 , 226 , 227 , 232 , 233 , 235 , 236 , 255 , 264

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

of order 64 and Hall-Senior numbers: 704 , 823 , 87 , 88 , 1453 , 149 , 190 , 191 , 199 , 227