Group #7:  Cyclic(2) x Quaternion(8)

Magma small group library number: 12

General information about the group

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

Center abelian of type: [ 2, 2 ]

Orders of the terms of the Lower Central Series: [ 16, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 4, 16 ]

Order of the Frattini Subgroup: 2

Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 16 ]

SUPERGROUPS AND SUPERQUOTIENTS

The subindices indicate multiplicities.

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

of order 32 and Hall-Senior numbers: 912 , 10 , 15 , 24 , 252 , 28 , 352 , 37 , 39 , 435 , 45 , 48

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

of order 32 and Hall-Senior numbers: 96 , 12 , 15 , 352 , 37 , 40