GAP Manual: 48.6. TestCharTable

TestCharTable( tbl )

checks the character table tbl:
if tbl.centralizers, tbl.classes, tbl.orders and the entries of tbl.powermap have same length,
if the product of tbl.centralizers[i] with tbl.classes[i] is equal to tbl.order,
if tbl.orders[i] divides tbl.centralizers[i],
if the entries of tbl.classnames and the corresponding record fields are consistent,
if the first orthogonality relation for tbl.irreducibles is satisfied,
if the centralizers agree with the sums of squared absolute values of tbl.irreducibles and
if powermaps and representative orders are consistent.

If no inconsistency occurs, true is returned, otherwise each error is signalled, and false is returned at the end.

    gap> t:= CharTable("A5");; TestCharTable(t);
    true
    gap> t.irreducibles[2]:= t.irreducibles[3] - t.irreducibles[1];;
    gap> TestCharTable(t);
    #E TestCharTable(A5): Scpr( ., X[2], X[1] ) = -1
    #E TestCharTable(A5): Scpr( ., X[2], X[2] ) = 2
    #E TestCharTable(A5): Scpr( ., X[3], X[2] ) = 1
    #E TestCharTable(A5): centralizer orders inconsistent with irreducibles
    false