Finite Group Databasebeta

← Group #10612221

Character table — Group #10612221

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size1111222222222222444444444444444888888888888888888888101010101010101016161616202020202020404040
order1222444455101010101010444888820202020202020204442020202020202020202040404040404040402222888820202020444488444
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1111111111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111
χ41111111111111111111-1-1-1-1111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1
χ511111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-111-1-1-1
χ611111111111111111-1-1111111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111
χ711111111111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11-1-1
χ811111111111111111-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-111
χ91111-1-11111111111-11111-1-1-1-1-1-11111-11-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-11-111-1-1-11-1
χ101111-1-11111111111-11111-1-1-1-1-1-11111-11-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1-11-1-1111-11
χ111111-1-11111111111-111-1-111-1-1-1-11111-1-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-11111-1
χ121111-1-11111111111-111-1-111-1-1-1-11111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-111-1111-1-1-1-11
χ131111-1-11111111111-1-1-111-1-1-1-1-1-111111-11-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1111-1-1-1-1-11-11
χ141111-1-11111111111-1-1-111-1-1-1-1-1-111111-11-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-111111-11-1
χ151111-1-11111111111-1-1-1-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11-11111-1-11
χ161111-1-11111111111-1-1-1-1-111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-11-1-1-1-111-1
χ1722222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222222−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000−1+52−1−52−1+52−1−52000000000
χ1822222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222-2-2-2-2−1+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+52−1−52−1−521−521−521+521+521−521−521+521+52000000001−521+521−521+52000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-22222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000001−521+521−521+52000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-222−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000−1+52−1−52−1+52−1−52000000000
χ2122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000−1−52−1+52−1−52−1+52000000000
χ2222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+522-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000001+521−521+521−52000000000
χ2322222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-22222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000001+521−521+521−52000000000
χ2422222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-222−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000−1−52−1+52−1−52−1+52000000000
χ25222222-2-222222222-20000002222-2-2-2-2000-2-20000000000000000222200000000-2-20000000
χ26222222-2-222222222-20000002222-2-2-2-2000-2-20000000000000000-2-2-2-200000000220000000
χ272222-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-22222-2-21−521−521+521+52−1+52−1−52−1+52−1−52-22-21−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000−1+52−1−521−521+52000000000
χ282222-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-222-2-2221−521−521+521+52−1+52−1−52−1+52−1−52-2-221−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000001−521+52−1+52−1−52000000000
χ292222-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-222-2-21−521−521+521+52−1+52−1−52−1+52−1−522-221−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000001−521+52−1+52−1−52000000000
χ302222-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2221−521−521+521+52−1+52−1−52−1+52−1−5222-21−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000−1+52−1−521−521+52000000000
χ312222-2-222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-22222-2-21+521+521−521−52−1−52−1+52−1−52−1+52-22-21+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000000−1−52−1+521+521−52000000000
χ322222-2-222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-222-2-2221+521+521−521−52−1−52−1+52−1−52−1+52-2-221+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+52000000001+521−52−1−52−1+52000000000
χ332222-2-222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-222-2-21+521+521−521−52−1−52−1+52−1−52−1+522-221+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000001+521−52−1−52−1+52000000000
χ342222-2-222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2221+521+521−521−52−1−52−1+52−1−52−1+5222-21+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+5200000000−1−52−1+521+521−52000000000
χ352222-2-2-2-2222222222000000-2-2-2-2-2-2-2-200022000000000000000022-2-200000000-220000000
χ362222-2-2-2-2222222222000000-2-2-2-2-2-2-2-2000220000000000000000-2-222000000002-20000000
χ3722-2-22-2002222-2-2-2-20002−22−22-22-2000000000000000002−22−22−22−22-22-222−2−2000000002−2000
χ3822-2-22-2002222-2-2-2-20002−22−22-22-2000000000000000002−22−22−22−2-22-22−2−22200000000−22000
χ3922-2-22-2002222-2-2-2-2000−22−222-22-200000000000000000−22−22−22−222-22-2−2−22200000000−22000
χ4022-2-22-2002222-2-2-2-2000−22−222-22-200000000000000000−22−22−22−22-22-2222−2−2000000002−2000
χ4122-2-2-22002222-2-2-2-20002−2−22-22-22000000000000000002−22−2−22−222-2-2222−2−200000000−22000
χ4222-2-2-22002222-2-2-2-20002−2−22-22-22000000000000000002−22−2−22−22-222-2−2−222000000002−2000
χ4322-2-2-22002222-2-2-2-2000−222−2-22-2200000000000000000−22−222−22−22-2-22−2−222000000002−2000
χ4422-2-2-22002222-2-2-2-2000−222−2-22-2200000000000000000−22−222−22−2-222-222−2−200000000−22000
χ452-2-2200-2222-2-2-2-22202-200000000-2-2220000000002-22-20000000000002-22-20000002-200000
χ462-2-2200-2222-2-2-2-22202-200000000-2-2220000000002-22-2000000000000-22-22000000-2200000
χ472-2-2200-2222-2-2-2-2220-2200000000-2-222000000000-22-220000000000002-22-2000000-2200000
χ482-2-2200-2222-2-2-2-2220-2200000000-2-222000000000-22-22000000000000-22-220000002-200000
χ49444444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4000000−1+5−1+5−1−5−1−51−51+51−51+50001−51+50000000000000000000000000000000000000
χ50444444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4000000−1−5−1−5−1+5−1+51+51−51+51−50001+51−50000000000000000000000000000000000000
χ514444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−540000001−51−51+51+51−51+51−51+5000−1+5−1−50000000000000000000000000000000000000
χ524444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+540000001+51+51−51−51+51−51+51−5000−1−5−1+50000000000000000000000000000000000000
χ5344-4-44-400−1+5−1−5−1+5−1−51−51+51−51+500022−2222−22−1+51−5−1−51+500000000000000000−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+ζ39000000000000000000000
χ5444-4-44-400−1+5−1−5−1+5−1−51−51+51−51+5000−2222−2222−1+51−5−1−51+500000000000000000ζ7−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−ζ39000000000000000000000
χ5544-4-44-400−1−5−1+5−1−5−1+51+51−51+51−500022−2222−22−1−51+5−1+51−500000000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000000000
χ5644-4-44-400−1−5−1+5−1−5−1+51+51−51+51−5000−2222−2222−1−51+5−1+51−500000000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000000000
χ5744-4-4-4400−1+5−1−5−1+5−1−51−51+51−51+500022−22−22221−5−1+51+5−1−500000000000000000−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−ζ39000000000000000000000
χ5844-4-4-4400−1+5−1−5−1+5−1−51−51+51−51+5000−222222−221−5−1+51+5−1−500000000000000000ζ7−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+ζ39000000000000000000000
χ5944-4-4-4400−1−5−1+5−1−5−1+51+51−51+51−500022−22−22221+5−1−51−5−1+500000000000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37000000000000000000000
χ6044-4-4-4400−1−5−1+5−1−5−1+51+51−51+51−5000−222222−221+5−1−51−5−1+500000000000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37000000000000000000000
χ614-44-4000044-4-444-4-4000000000000000000000000000000000000000022−22−22220000000000000
χ624-44-4000044-4-444-4-40000000000000000000000000000000000000000−222222−220000000000000
χ634-4-44004-444-4-4-4-4440000000000044-4-4000000000000000000000000000000000000000000
χ644-4-44004-4−1+5−1−51−51+51−51+5−1+5−1−500000000000−1+5−1−51−51+500000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000000000
χ654-4-44004-4−1+5−1−51−51+51−51+5−1+5−1−500000000000−1+5−1−51−51+5000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000000000
χ664-4-44004-4−1−5−1+51+51−51+51−5−1−5−1+500000000000−1−5−1+51+51−5000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000000000
χ674-4-44004-4−1−5−1+51+51−51+51−5−1−5−1+500000000000−1−5−1+51+51−500000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000000000
χ684-4-4400-44−1+5−1−51−51+51−51+5−1+5−1−504-4000000001−51+5−1+5−1−5000000000−1+51−5−1−51+500000000000000000000000000000
χ694-4-4400-44−1+5−1−51−51+51−51+5−1+5−1−50-44000000001−51+5−1+5−1−50000000001−5−1+51+5−1−500000000000000000000000000000
χ704-4-4400-44−1−5−1+51+51−51+51−5−1−5−1+504-4000000001+51−5−1−5−1+5000000000−1−51+5−1+51−500000000000000000000000000000
χ714-4-4400-44−1−5−1+51+51−51+51−5−1−5−1+50-44000000001+51−5−1−5−1+50000000001+5−1−51−5−1+500000000000000000000000000000
χ728-88-80000−2+25−2−252−252+25−2+25−2−252−252+25000000000000000000000000000000000000000000000000000000000
χ738-88-80000−2−25−2+252+252−25−2−25−2+252+252−25000000000000000000000000000000000000000000000000000000000

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