Cayley diagrams of groups of genus 1

The pink arrows around the edge of each diagram are "sewing instructions", showing how it is to be assembled into a genus 1 surface, or torus. The light pink regions are to be "discarded" once the sewing has been done.

A4

A4

A4×C2

A4×C2

A4×C2

A4×C2

SL(2,3)

SL(2,3)

S4

(C3×C3)⋊C3

(C3×C3)⋊C3

(C3×C3)⋊C2

(C3×C3)⋊C2

(C2×C2)⋊C4

(C2×C2)⋊C4

quasidihedral, order 16

quasidihedral 16

modular, order 16

modular 16

pauli

Pauli

pauli

Pauli

C4⋊C4

C4⋊C4

C4×C7, as an example of the many groups of the form Cm×Cn

C4×C7

Q8

Q8

Q28, as an example of the many dicyclic groups

Q28

C3⋊C8

C3⋊C8

C3⋊D8

C3⋊D8

C2×D14, as an example of the many groups of the form C2×D2n

C2×D14n

C2×C2×C2×C2

C2×C2×C2×C2

Q8×C3

Q8×C3

C7×C2×C2, as an example of the many groups of the form C2×C2×Cn

C7×C2×C2

C5×D6, as an example of the many groups of the form Cn×D2n

C5×D6

(C2×C2)⋊C4

(C2×C2)⋊C4

C5⋊C4, the Frobenius group of order 20

C5⋊C4, Frobenius 20

(C3xC3)⋊C2

(C3xC3)⋊C2

C7⋊C3

C7⋊C3, Frobenius 21

C7⋊C6, the Frobenius group of order 42

C7⋊C6, Frobenius 42

Regular maps drawn on the torus.
Some more Cayley diagrams drawn on surfaces appropriate to their genus.
Some more Cayley diagrams
and other pages on groups
Copyright N.S.Wedd 2009