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.

Groups of order 4 6 8 9 10 12 14 15 16 18 20 21 22 24 25 27 28 30 48 60 120 168 336 360 720

Index to regular maps