Group #14:  Cyclic(4) x Dihedral(8)

Magma small group library number: 25

General information about the group

PC-Group relations:
g12 = g3	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: 4

Exponent of G: 4

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

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 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: 188 , 276 , 34 , 552 , 56 , 62 , 774 , 784 , 803 , 99 , 100 , 1068 , 1076 , 1172 , 118 , 1542 , 1553 , 1572 , 1583 , 1593 , 1602 , 1613 , 1632 , 1644 , 1654 , 1662 , 167 , 168 , 1752 , 1762 , 1772 , 178 , 205 , 207 , 208 , 209 , 219 , 221

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

of order 64 and Hall-Senior numbers: 184 , 284 , 292 , 34 , 55 , 56 , 57 , 58 , 842 , 852 , 862 , 88 , 912 , 92 , 99 , 100 , 117 , 118 , 119 , 122