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
Non-orientable
projective plane
|
4
|
5
|
6
|
7