Group #36

Magma small group library number: 28

General information about the group

PC-Group relations:
g22 = g4	g1-1 g2 g1 = g2 g4
g1-1 g3 g1 = 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: [ 8, 8, 8 ]

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32, 32, 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: 718 , 772 , 784 , 80 , 1544 , 1573 , 1586 , 1593 , 1602 , 1644 , 1664 , 1694 , 1704 , 1718 , 1753 , 1766 , 177 , 178 , 1846 , 1854 , 1952 , 196 , 201 , 203 , 213 , 214 , 217 , 223 , 2282 , 229 , 237

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

of order 64 and Hall-Senior numbers: 714 , 832 , 842 , 852 , 88 , 91 , 1443 , 1463 , 149 , 1503 , 151 , 195 , 196 , 197 , 205 , 206 , 208 , 211 , 219 , 220 , 228 , 229 , 230 , 256 , 257 , 258