Group #10:  Cyclic(2) x AlmostExtraSpecial(16)

Magma small group library number: 48

General information about the group

PC-Group relations:
g32 = g5	g2-1 g4 g2 = 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: 2

Exponent of G: 4

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

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32, 32, 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: 1424 , 21 , 27 , 462 , 51 , 53 , 77 , 782 , 96 , 1036 , 10410 , 10515 , 107 , 109 , 110 , 111 , 1122 , 114 , 120 , 126 , 127 , 157 , 1582 , 159 , 1602 , 170 , 1712 , 172 , 217 , 218

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

of order 64 and Hall-Senior numbers: 146 , 18 , 19 , 202 , 272 , 71 , 72 , 732 , 742 , 752 , 763 , 772 , 782 , 792 , 803 , 157 , 158 , 159 , 160 , 161 , 162 , 1632 , 1642 , 1652 , 1662 , 1672 , 1682 , 175 , 176 , 177 , 178 , 179