Group #6:  Cyclic(2) x Dihedral(8)

Magma small group library number: 11

General information about the group

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

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 16, 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: 812 , 103 , 14 , 232 , 24 , 27 , 333 , 346 , 363 , 38 , 39 , 429 , 44 , 46 , 47

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

of order 32 and Hall-Senior numbers: 86 , 112 , 12 , 14 , 23 , 24 , 25 , 26 , 333 , 343 , 35 , 362 , 37 , 38 , 39 , 44 , 45