Group #31

Magma small group library number: 11

General information about the group

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

Center abelian of type: [ 4 ]

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

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

Order of the Frattini Subgroup: 8

Exponent of G: 8

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

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16, 8 ]

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32, 16 ]

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: 514 , 582 , 1204 , 1222 , 2612 , 2622 , 2632 , 2642

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

of order 64 and Hall-Senior numbers: 512 , 602 , 62 , 63 , 237 , 238 , 2392 , 2402