Group #9

Magma small group library number: 3

General information about the group

PC-Group relations:
g12 = g3	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: 4

Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 8 ]

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

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: 114 , 142 , 162 , 333 , 362 , 372 , 383 , 394 , 413 , 462

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

of order 32 and Hall-Senior numbers: 114 , 183 , 20 , 27 , 28 , 31 , 46 , 47 , 48