Group #11

Magma small group library number: 6

General information about the group

PC-Group relations:
g12 = g2	g22 = g4	g1-1 g3 g1 = g3 g4

Center abelian of type: [ 4 ]

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: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]

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: 134 , 173 , 31 , 322 , 44 , 45 , 472 , 482

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

of order 32 and Hall-Senior numbers: 132 , 192 , 20 , 21