Group #8:  AlmostExtraSpecial(16)

Magma small group library number: 13

General information about the group

PC-Group relations:
g22 = g4	g32 = g4	g1-1 g3 g1 = g3 g4

Center abelian of type: [ 4 ]

Orders of the terms of the Lower Central Series: [ 16, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 4, 16 ]

Order of the Frattini Subgroup: 2

Exponent of G: 4

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

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

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

SUPERGROUPS AND SUPERQUOTIENTS

The subindices indicate multiplicities.

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

of order 32 and Hall-Senior numbers: 108 , 17 , 262 , 31 , 426 , 4310 , 44 , 45

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

of order 32 and Hall-Senior numbers: 102 , 14 , 15 , 162 , 36 , 37 , 382 , 392 , 402 , 413