Group #29

Magma small group library number: 14

General information about the group

PC-Group relations:
g12 = g2	g32 = g4 g5	g42 = g5
g1-1 g3 g1 = g3 g4		g1-1 g4 g1 = g4 g5

Center abelian of type: [ 2, 2 ]

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

Orders of the terms of the Upper Central Series: [ 1, 4, 8, 32 ]

Order of the Frattini Subgroup: 8

Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32 ]

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 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: 494 , 542 , 55 , 57 , 1162 , 118 , 138 , 139 , 1402 , 1412 , 1904 , 195 , 197 , 1992 , 2072 , 2122 , 2132 , 2162 , 221 , 222 , 223 , 224 , 2272 , 229

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

of order 64 and Hall-Senior numbers: 494 , 59 , 64 , 140 , 141 , 143