Group #37

Magma small group library number: 29

General information about the group

PC-Group relations:
g12 = g4	g22 = g4	g1-1 g2 g1 = g2 g4
g1-1 g3 g1 = 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: [ 8 ]

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

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: 728 , 772 , 794 , 80 , 1556 , 157 , 1593 , 1602 , 1616 , 1632 , 1672 , 1682 , 1714 , 1724 , 17312 , 1744 , 175 , 1773 , 1783 , 1792 , 1854 , 1864 , 196 , 1972 , 202 , 204 , 215 , 216 , 218 , 224 , 229 , 2302 , 238

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

of order 64 and Hall-Senior numbers: 724 , 832 , 862 , 872 , 88 , 92 , 1453 , 1473 , 1483 , 1492 , 1503 , 152 , 207 , 209 , 210 , 212 , 221 , 222