general linear group
symmetric group, cyclic group, braid group
classification of finite simple groups
sporadic finite simple groups
compact topological group, locally compact topological group
maximal compact subgroup
compact Lie group
super Lie group
super Euclidean group
k-tuply groupal n-groupoid
circle n-group, string 2-group, fivebrane Lie 6-group
∞-group extension, Ext-group
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A quotient group is a quotient object in the category Grp of groups.
For G a group and H↪G a normal subgroup, the quotient group G/H is the set of cosets, equipped with a group structure induced from G.