{ "date":"13.09.2023", "comment":[ "The data records are arrays of length 5 or 6.", "The first four entries of each record are the character name,", "the character position, the degree of the character field,", "and a string describing the OD.", "The last entry is a string that lists how the OD was computed,", "as a comma separated sequence of flags.", "For non-simple groups in characteristic 2,", "the record has length 6, and position 5 describes whether", "the matrix group embeds in the simple orthogonal group (value S+)", "or not (value S-).", "The flags listed in the last column mean the following:", "- AGR: verified using the Atlas of Group Representations", "- RP: verified using a representations constructed by Richard Parker", "- const(): verified using a constituent of the reduction of ", " (a permutation representation from the AGR)", "- order: group order divides the order of only one relevant O+/O- group", "- permchar: chi+1 is a 2-trans. permutation character", "- lift: the p-modular OD arises from the ordinary OD", "- lift(+...): the p-modular OD arises from the ordinary OD and known ODs", "- ev: there is a group element without eigenvalues +-1", "- ext(...): the OD of the restriction to a subgroup is known", "- rest(...): the character is the restriction from an overgroup", "- specht: verified using the Jantzen-Schaper formula", "- syl(

): verified by orth. stable restriction to a Sylow

-subgroup" ], "names":["A5","L3(2)","A6","L2(8)","L2(11)","L2(13)","L2(17)","A7","L2(19)","L2(16)","L3(3)","U3(3)","L2(23)","L2(25)","M11","L2(27)","L2(29)","L2(31)","L3(4)","A8","U4(2)","Sz(8)","L2(32)","L2(49)","U3(4)","M12","U3(5)","J1","A9","L2(81)","L3(5)","M22","J2","S4(4)","S6(2)","A10","L3(7)","U4(3)","G2(3)","S4(5)","U3(8)","U3(7)","L4(3)","L5(2)","M23","U5(2)","L3(8)","2F4(2)'","A11","Sz(32)","L3(9)","U3(9)","HS","J3","U3(11)","O8+(2)","O8-(2)","3D4(2)","A12","M24","G2(4)","McL","A13","He","O7(3)","S6(3)","G2(5)","U6(2)","R(27)","L6(2)","S8(2)","Ru","Suz","ON","Co3","O8+(3)","O8-(3)","O10+(2)","O10-(2)","Co2","Fi22","HN","F4(2)","S10(2)","Ly","Th","Fi23","Co1"], "A5":{ "names":["A5","A5.2"], "A5":{ "0":[ ["4a",4,1,"5","OBGN,permchar,AGR,ev,ext(D10),rest(A5.2),syl(5),specht"]], "2":[ ["4a",4,1,"O-","RP,order,AGR,lift,syl(5)"]], "3":[ ["4a",4,1,"O-","RP,order,lift,AGR,ev,ext(D10),syl(5)"]], "5":[]}, "A5.2":{ "0":[ ["6a",3,1,"-5","ind(A5),ext(5:4),specht"], 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