Group #15:  Cyclic(4) x Quaternion(8)

Magma small group library number: 26

General information about the group

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

Center abelian of type: [ 2, 4 ]

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: 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: 198 , 272 , 35 , 56 , 572 , 63 , 794 , 80 , 101 , 1072 , 1088 , 118 , 1192 , 155 , 1566 , 158 , 159 , 161 , 1626 , 1652 , 167 , 1683 , 178 , 1792 , 206 , 210 , 211 , 212 , 220 , 222

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

of order 64 and Hall-Senior numbers: 194 , 292 , 35 , 872 , 88 , 92 , 101