Group #50:  Semidihedral(32)

Magma small group library number: 19

General information about the group

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

Center abelian of type: [ 2 ]

Orders of the terms of the Lower Central Series: [ 32, 8, 4, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 2, 4, 8, 32 ]

Order of the Frattini Subgroup: 8

Exponent of G: 16

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]

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

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

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: 1354 , 1372 , 2442 , 2452

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

of order 64 and Hall-Senior numbers: 1352 , 138 , 139 , 1412