Group #47

Magma small group library number: 7

General information about the group

PC-Group relations:
g12 = g3	g32 = g5	g1-1 g2 g1 = g2 g4
g2-1 g3 g2 = g3 g5		g1-1 g4 g1 = g4 g5

Center abelian of type: [ 2 ]

Orders of the terms of the Lower Central Series: [ 32, 4, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 2, 8, 32 ]

Order of the Frattini Subgroup: 8

Exponent of G: 8

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: [ 32, 32 ]

SUPERGROUPS AND SUPERQUOTIENTS

The subindices indicate multiplicities.

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

of order 64 and Hall-Senior numbers: 1244 , 1272 , 250 , 251 , 2562 , 257 , 261 , 262

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

of order 64 and Hall-Senior numbers: 1242 , 129 , 131 , 234 , 236 , 239