A4

Also called PSL(2,3), tetrahedral group, (C2×C2) ⋊ C3, A₁(3).

Statistics
Order of group	12
GAP identifier	12,3
Presentation	< k,r \| k³, r², (kr)³ >
Orders of elements	1 of 1, 3 of 2, 2*4 of 3
Centre	1
Derived subgroup	C2×C2
Automorphism group	S4
Inner automorphism group	A4
"Out" (quotient of above)	C2
Schur multiplier	C2
Sylow-2-subgroup	C2×C2

Permutation Diagrams

Sharply 2-transitive
on 4 points, even.

Sharply 4-transitive
on 4 points, even.

1-transitive on 6
points, even.

1-transitive on 6
points, even.

1-transitive on 12
points, even.

Cayley Graphs

octahemioctahedron, type I

octahemioctahedron, type I

the tetrahedron, type II

the cuboctahedron, type I

the icosahedron, type I

rectification of {6,3}_(0,2), type I

Regular maps with A4 symmetry

A4 is the rotational symmetry group of the regular map the tetrahedron.

Index to regular maps