C3×C3×C3
C3×C3×C3
is Abelian, and is a direct product of two smaller groups
.
Statistics
Order of group
27
GAP identifier
27,5
Presentation
< k,r,g  k
^{3}
, r
^{3}
, g
^{3}
, [k,r], [r,g], [g,k] >
Orders of elements
1 of 1, 26*1 of 27
Centre
C3×C3×C3
Derived subgroup
1
Automorphism group
GL(3,3)
Inner automorphism group
1
"Out"
(quotient of above)
GL(3,3)
Schur multiplier
C3×C3×C3
Permutation Diagrams
Not transitive.
Cayley Graphs
Index to regular maps
Orientable
sphere

torus

2

3

4

5

6
Nonorientable
projective plane

4

5

6

7