Group #10

Magma small group library number: 4

General information about the group

PC-Group relations:
g12 = g3	g22 = 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: [ 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: 124 , 14 , 153 , 162 , 27 , 28 , 292 , 302 , 354 , 36 , 373 , 382 , 406 , 413

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

of order 32 and Hall-Senior numbers: 124 , 183 , 21 , 29 , 30 , 32