Group #21

Magma small group library number: 12

General information about the group

PC-Group relations:
g12 = g2	g22 = g3	g42 = g5
g1-1 g4 g1 = g4 g5

Center abelian of type: [ 2, 4 ]

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

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

Order of the Frattini Subgroup: 8

Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4 ]

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32 ]

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: 254 , 332 , 34 , 353 , 62 , 63 , 642 , 652 , 954 , 974 , 982 , 99 , 100 , 1013 , 1022 , 205 , 206 , 207 , 208 , 209 , 210 , 211 , 212 , 219 , 220 , 221 , 222 , 2342 , 2352 , 2362

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

of order 64 and Hall-Senior numbers: 254 , 372 , 41 , 64 , 65 , 67