Group #9:  Abelian(2,2) x Quaternion(8)

Magma small group library number: 47

General information about the group

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

Center abelian of type: [ 2, 2, 2 ]

Orders of the terms of the Lower Central Series: [ 32, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 8, 32 ]

Order of the Frattini Subgroup: 2

Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 8 ]

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: 1328 , 14 , 19 , 44 , 452 , 48 , 702 , 72 , 74 , 87 , 1045 , 108 , 111 , 115 , 125 , 145 , 147 , 1552 , 159 , 172 , 203 , 204

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

of order 64 and Hall-Senior numbers: 1314 , 16 , 19 , 702 , 72 , 75 , 79 , 155 , 1562 , 161 , 162 , 173 , 174