CREATE TABLE gps_crep (
	cyc_order_mat	integer,	-- an integer $m$ so that the entries in {{KNOWL('columns.gps_crep.gens', 'gens')}} lie in $\mathbb{Q}(\zeta_m)$
	cyc_order_traces	integer,	-- an integer $m$ so that the entries in {{KNOWL('columns.gps_crep.traces', 'traces')}} lie in $\mathbb{Q}(\zeta_m)$
	decomposition	jsonb,	-- List of triples `(label, m)` where `label` is the label of a subgroup of lower dimension and $m$ is the multiplicity
	denominators	_int4,	-- A list of denominators for the matrix images, with the order matching the generators in the `gps_groups` table.
	dim	smallint,	-- The dimension: the $n$ for which this is a subgroup of $\operatorname{GL}_n(\mathbb{C})$
	gens	jsonb,	-- A list of scaled matrices generating the group, with the order matching {{KNOWL('columns.gps_groups.perm_gens', 'perm_gens')}} for the group (in the non-solvable case) or the {{KNOWL('columns.gps_groups.pc_code', 'presentation')}} (in the solvable case). The entries are encoded as lists of pairs `(c, e)` representing the sum of $c \zeta_m^e$ (divided by the corresponding {{KNOWL('columns.gps_crep.denominators', 'denominator')}}). Here $m$ is the value of {{KNOWL('columns.gps_crep.cyc_order_mat', 'cyc_order_mat')}}, $c \ge 0$ and $0 \le 2e < m$.
	group	text,	-- The {{KNOWL('group.label', 'label')}} of the abstract group
	id	bigint,	-- 
	indicator	smallint,	-- the Frobenius-Schur indicator
	irreducible	boolean,	-- whether this subgroup is irreducible
	label	text,	-- label of the first character having this group as its image
	order	numeric,	-- The order of the group
	schur_index	smallint,	-- The ratio of the minimal degree of a number field containing all {{KNOWL('columns.gps_crep.gens', 'matrix entries')}} by the degree of the number field generated by the {{KNOWL('columns.gps_crep.traces', 'traces')}}
	trace_field	_numeric,	-- list of coefficients of a polynomial defining the field generated by the traces. This will be polredabs'ed unless the degree is at least 90.
	traces	jsonb 	-- The traces of the conjugacy classes (in the order of {{KNOWL('columns.gps_groups_cc.counter', 'gps_groups_cc')}}), encoded as lists of pairs `(c, e)` as in {{KNOWL('columns.gps_crep.gens', 'gens')}}, but using the $m$ from {{KNOWL('columns.gps_crep.cyc_order_traces', 'cyc_order_traces')}}.
);