C4×C2×C2
C4×C2×C2
is Abelian, and is a direct product of two smaller groups
.
Statistics
Order of group
16
GAP identifier
16,10
Presentation
< p,q,r  p
^{4}
, q
^{2}
, r
^{2}
, [p,q], [q,r], [r,p] >
Orders of elements
1 of 1, 1+6*1 of 2, 8*1 of 4
Centre
C4×C2×C2
Derived subgroup
1
Automorphism group
a group of order 192
Inner automorphism group
1
"Out"
(quotient of above)
a group of order 192
Schur multiplier
C2
Permutation Diagrams
Not transitive.
Not transitive.
Cayley Graphs
{4,4}
_{(4,0)}
, type I
Index to regular maps
Orientable
sphere

torus

2

3

4

5

6
Nonorientable
projective plane

4

5

6

7