Group #33

Magma small group library number: 27

General information about the group

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

Center abelian of type: [ 2, 2 ]

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

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

Order of the Frattini Subgroup: 4

Exponent of G: 4

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

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16, 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: 688 , 772 , 1544 , 1572 , 163 , 1694 , 1704 , 1752 , 1836 , 1843 , 250 , 2593

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

of order 64 and Hall-Senior numbers: 684 , 814 , 84 , 86 , 1443 , 145 , 146 , 147 , 201 , 202 , 203 , 204 , 217 , 218 , 259 , 260 , 261 , 262 , 263 , 264