Group #41

Magma small group library number: 33

General information about the group

PC-Group relations:
g22 = g5	g32 = g4 g5	g1-1 g2 g1 = g2 g4 g5
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: [ 8 ]

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

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: 768 , 802 , 1632 , 1642 , 1672 , 1684 , 1752 , 1772 , 1782 , 1794 , 1842 , 1864

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

of order 64 and Hall-Senior numbers: 764 , 91 , 92 , 934 , 150 , 1512 , 1522 , 1537