C9×C3
C9×C3
is Abelian, and is a direct product of two smaller groups
.
Statistics
Order of group
27
GAP identifier
27,2
Presentation
< k,r  k
^{9}
, r
^{3}
, [k,r] >
Orders of elements
1 of 1, 8*1 of 3, 18*1 of 9
Centre
C9×C3
Derived subgroup
1
Automorphism group
a group of order 108
Inner automorphism group
1
"Out"
(quotient of above)
a group of order 108
Schur multiplier
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