CREATE TABLE gps_conj_classes (
	aut_label	text,	-- Label for the first conjugacy class in the orbit of this one under the automorphism group.  May be null if not computed
	centralizer	text,	-- The {{KNOWL('group.subgroup_label', 'label')}} of the {{KNOWL('group.centralizer', 'centralizer')}} of elements in this conjugacy class
	counter	integer,	-- An integer giving a {{KNOWL('group.label_conjugacy_class', 'total order')}} on conjugacy classes within the same group.
	group_counter	integer,	-- Counter for the ambient group (1-based)
	group_order	numeric,	-- Order of the ambient group
	id	integer,	-- 
	label	text,	-- The {{KNOWL('group.label_conjugacy_class', 'label')}} of this conjugacy class
	order	integer,	-- The {{KNOWL('group.element_order', 'order')}} of elements in this conjugacy class
	powers	_int4,	-- For each prime $p$ dividing the {{KNOWL('group.order', 'order')}} of the group or the Euler $\phi$ function of the {{KNOWL('group.exponent', 'exponent')}} of the group, the {{KNOWL('columns.gps_groups_cc.counter', 'counter')}} for the conjugacy class containing the $p$-th power of an element in this conjugacy class.
	representative	numeric,	-- An encoded representative for this conjugacy class, using the group's {{KNOWL('columns.gps_groups_cc.elt_rep_type', 'elt_rep_type')}}
	size	numeric 	-- The number of elements in this conjugacy class
);