Warning

Many parts work with explorer, but some do not (due to bugs in explorer). For example, zooming the size of the table, picking groups by order, and picking groups from the misc. list do not work in explorer.

Instructions

• Select a group.
• Click on elements from the special left column to select/deselect them.
• Explore subgroups generated by a set of elements by selecting them and then clicking on Generate Subgroup
• Explore orders of elements by selecting one element, and then generating its (cyclic) subgroup.
• Explore conjugacy classes by selecting an element, and then clicking to Close Under Conj.
• Generate normal subgroups by combining Generate Subgroup and Close Under Conj.
• When you Generate Subgroup, the group table is reorganized by left coset, and colored accordingly. You should be able to see if the subgroup is normal, and the group table for the quotient group.

Notes on Group Notations

• One can enter an abitrary product of cyclic groups using the "Zn1 x Zn2 x ..." type. Enter the sizes of the factors as a comma-separated list when the blank is offered.
• A group "Aff(Z_n)" is the set of affine functions ax+b where a and b are taken in Z_n, and a relatively prime to n. It is a group under composition.
• For dihedral groups, a special notation is used for reflections when n=3 or 4 (representing the line being reflected over). For larger dihedral groups, v_j is the reflection which sends vertex 1 to vertex j.