Finite Group Databasebeta

← Group #10612136

Character table — Group #10612136

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size111122222222222244444444444888888888888888888888881616161620202020202020202020404040
order1222444455101010101010444202020202020202022488202020202020202020204040404040404040101010102222448888224
χ11111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1
χ4111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ511111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
χ611111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1
χ711111111111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1
χ811111111111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111
χ91111-1-11111111111-111-1-1-1-111111-1-11-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1111-1-1-1111-1-1
χ101111-1-11111111111-111-1-1-1-111111-1-11-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11-1-1-1111-1-1-111
χ111111-1-11111111111-111-1-1-1-11111-11-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-1-11-111-1-11-11
χ121111-1-11111111111-111-1-1-1-11111-11-1-11-1-11111-1-1-1-1-1-1-1-11111-1-111-1111-11-1-111-11-1
χ131111-1-11111111111-1-1-1-1-1-1-111111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-11-1111-111-1-1-11-1
χ141111-1-11111111111-1-1-1-1-1-1-111111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-1-11-1-1111-11
χ151111-1-11111111111-1-1-1-1-1-1-11111-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-11-1-1-111-111
χ161111-1-11111111111-1-1-1-1-1-1-11111-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1111-1111-1-11-1-1
χ1722222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−520000000000000
χ1822222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-22-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521+521−521+520000000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222-2-2-2−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−520000000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2-222−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+520000000000000
χ2122222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+520000000000000
χ2222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-22-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521−521+521−520000000000000
χ2322222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222-2-2-2−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+520000000000000
χ2422222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2-222−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−520000000000000
χ25222222-2-222222222-2002222-2-2-2-200000-2-2000000000000000000002200-2-20000000
χ26222222-2-222222222-2002222-2-2-2-200000-2-200000000000000000000-2-200220000000
χ272222-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2221−521−521+521+52−1+52−1−52−1+52−1−522-2-22-21−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+520000000000000
χ282222-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2221−521−521+521+52−1+52−1−52−1+52−1−52-22-2-221−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−520000000000000
χ292222-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+52−1+52−1−52−1+52−1−522-22-221−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+520000000000000
χ302222-2-222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+521+52−1+52−1−52−1+52−1−52-2222-21−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−520000000000000
χ312222-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2221+521+521−521−52−1−52−1+52−1−52−1+522-2-22-21+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−520000000000000
χ322222-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2221+521+521−521−52−1−52−1+52−1−52−1+52-22-2-221+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+520000000000000
χ332222-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−52−1−52−1+52−1−52−1+522-22-221+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−520000000000000
χ342222-2-222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-21+521+521−521−52−1−52−1+52−1−52−1+52-2222-21+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+520000000000000
χ352222-2-2-2-222222222200-2-2-2-2-2-2-2-20000022000000000000000000002-200-220000000
χ362222-2-2-2-222222222200-2-2-2-2-2-2-2-2000002200000000000000000000-22002-20000000
χ372-2-2200-2222-2-22-22-202-20000-2-22200000002-22-20000000000000000002-200002-2000
χ382-2-2200-2222-2-22-22-202-20000-2-22200000002-22-2000000000000000000-220000-22000
χ392-2-2200-2222-2-22-22-20-220000-2-2220000000-22-220000000000000000002-20000-22000
χ402-2-2200-2222-2-22-22-20-220000-2-2220000000-22-22000000000000000000-2200002-2000
χ41444444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-400−1+5−1+5−1−5−1−51−51+51−51+5000001−51+5000000000000000000000000000000000
χ42444444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-400−1−5−1−5−1+5−1+51+51−51+51−5000001+51−5000000000000000000000000000000000
χ434444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−54001−51−51+51+51−51+51−51+500000−1+5−1−5000000000000000000000000000000000
χ444444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+54001+51+51−51−51+51−51+51−500000−1−5−1+5000000000000000000000000000000000
χ4544-4-4000044-4-4-44-440000000000000000000000000000000000000000000022−2200000
χ4644-4-4000044-4-4-44-4400000000000000000000000000000000000000000000−222200000
χ474-44-44-4004444-4-4-4-40004-44-400000000000000000000000000000000000000000000
χ484-44-44-400−1+5−1−5−1+5−1−51−51−51+51+5000−1+51−5−1−51+50000000000000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ3900000000000000000
χ494-44-44-400−1+5−1−5−1+5−1−51−51−51+51+5000−1+51−5−1−51+50000000000000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ3900000000000000000
χ504-44-44-400−1−5−1+5−1−5−1+51+51+51−51−5000−1−51+5−1+51−50000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ3700000000000000000
χ514-44-44-400−1−5−1+5−1−5−1+51+51+51−51−5000−1−51+5−1+51−50000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ3700000000000000000
χ524-44-4-44004444-4-4-4-4000-44-4400000000000000000000000000000000000000000000
χ534-44-4-4400−1+5−1−5−1+5−1−51−51−51+51+50001−5−1+51+5−1−50000000000000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ3900000000000000000
χ544-44-4-4400−1+5−1−5−1+5−1−51−51−51+51+50001−5−1+51+5−1−50000000000000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ3900000000000000000
χ554-44-4-4400−1−5−1+5−1−5−1+51+51+51−51−50001+5−1−51−5−1+50000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ3700000000000000000
χ564-44-4-4400−1−5−1+5−1−5−1+51+51+51−51−50001+5−1−51−5−1+50000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ3700000000000000000
χ574-4-44004-444-4-44-44-4000000044-4-40000000000000000000000000000000000000000
χ584-4-44004-4−1+5−1−51−51+5−1+51−5−1−51+50000000−1+5−1−51−51+500000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000
χ594-4-44004-4−1+5−1−51−51+5−1+51−5−1−51+50000000−1+5−1−51−51+5000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000
χ604-4-44004-4−1−5−1+51+51−5−1−51+5−1+51−50000000−1−5−1+51+51−5000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000000000
χ614-4-44004-4−1−5−1+51+51−5−1−51+5−1+51−50000000−1−5−1+51+51−500000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000000000
χ624-4-4400-44−1+5−1−51−51+5−1+51−5−1−51+504-400001−51+5−1+5−1−50000000−1+51−5−1−51+500000000000000000000000000000
χ634-4-4400-44−1+5−1−51−51+5−1+51−5−1−51+50-4400001−51+5−1+5−1−500000001−5−1+51+5−1−500000000000000000000000000000
χ644-4-4400-44−1−5−1+51+51−5−1−51+5−1+51−504-400001+51−5−1−5−1+50000000−1−51+5−1+51−500000000000000000000000000000
χ654-4-4400-44−1−5−1+51+51−5−1−51+5−1+51−50-4400001+51−5−1−5−1+500000001+5−1−51−5−1+500000000000000000000000000000
χ6688-8-80000−2+25−2−252−252+252−25−2+252+25−2−25000000000000000000000000000000000000000000000000000
χ6788-8-80000−2−25−2+252+252−252+25−2−252−25−2+25000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1).