C4×C4
C4×C4
is Abelian, and is a direct product of two smaller groups
.
Statistics
Order of group
16
GAP identifier
16,2
Presentation
< k,r  k
^{4}
, r
^{4}
, [k,r] >
Orders of elements
1 of 1, 3*1 of 2, 12*1 of 4
Centre
C4×C4
Derived subgroup
1
Automorphism group
(C2×C2,A4) ⋊ C2
Inner automorphism group
1
"Out"
(quotient of above)
(C2×C2,A4) ⋊ C2
Schur multiplier
C4
Permutation Diagrams
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