Group #26

Magma small group library number: 42

General information about the group

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

Center abelian of type: [ 4 ]

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: 4

Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4, 4, 4 ]

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16, 8, 8 ]

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32, 16, 16 ]

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: 468 , 58 , 1124 , 122 , 1372 , 142 , 2413 , 2423 , 2433 , 244 , 245 , 248

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

of order 64 and Hall-Senior numbers: 462 , 532 , 542 , 55 , 56 , 57 , 195 , 196 , 197 , 1982 , 1992 , 2002 , 217 , 218 , 219 , 220 , 221 , 222 , 223 , 224