C2×C2

Also called  Klein.

C2×C2 is Abelian, and is a direct product of two smaller groups.

Statistics

Order of group4
GAP identifier4,2
Presentation< r, g | r2, g2, (rg)2 >
Orders of elements1 of 1, 3*1 of 2
CentreC2×C2
Derived subgroup1
Automorphism groupD6
Inner automorphism group1
"Out" (quotient of above)D6
Schur multiplierC2
 

Permutation Diagrams


Sharply 1-transitive
on 4 points, even.

Not transitive.

Cayley Graphs



the 2-hosohedron, type II

the tetrahedron, type I


{4,4}(2,0), type I

Regular maps with C2×C2 symmetry

C2×C2 is the rotational symmetry group of the regular maps the 2-hosohedron,   the hemi-2-hosohedron.

C2×C2 is the full symmetry group of the regular maps the monodigon,   the 1-lucanicohedron,   the dimonogon.


Index to regular maps

Orientable sphere | torus | 2 | 3 | 4 | 5 | 6
Non-orientable projective plane | 4 | 5 | 6 | 7