Finite Group Databasebeta

← Group #10612074

Character table — Group #10612074

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222222222224444444444444888888888888888888888810101010101016161616202020202040404040
order1222444455101010101010488882020202020202020222410101010202020202020404040404040404022444410101010488884444
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111-1
χ611111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-11
χ711111111111111111-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-1-11-1-11
χ811111111111111111-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ91111-1-11111111111-111-1-111-1-1-1-1111-11-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-1-11-11
χ101111-1-11111111111-111-1-111-1-1-1-1111-11-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1111-11-1
χ111111-1-11111111111-111-1-111-1-1-1-111-11-11-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-111-1-11-11-1
χ121111-1-11111111111-111-1-111-1-1-1-111-11-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-111-11-11
χ131111-1-11111111111-1-1-11111-1-1-1-1111-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-11111-1-1
χ141111-1-11111111111-1-1-11111-1-1-1-1111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-111
χ151111-1-11111111111-1-1-11111-1-1-1-111-111-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1-111
χ161111-1-11111111111-1-1-11111-1-1-1-111-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111-1-111-1-1
χ1722222222−1+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+52−1−522222−1+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+52−1−52−1−52000000−1+52−1−52−1+52−1−52000000000
χ1822222222−1+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+52−1−52-2-2-2-21−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000001−521+521−521+52000000000
χ1922222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-21−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+52000000−1+52−1−52−1+52−1−52000000000
χ2022222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+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+520000001−521+521−521+52000000000
χ2122222222−1−52−1+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+522222−1−52−1−52−1+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+52000000−1−52−1+52−1−52−1+52000000000
χ2222222222−1−52−1+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+52-2-2-2-21+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000001+521−521+521−52000000000
χ2322222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-21+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52000000−1−52−1+52−1−52−1+52000000000
χ2422222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000001+521−521+521−52000000000
χ25222222-2-222222222-20000-2-22222-2-200000000-2-200000000000022-2-2-2-20000200000000
χ26222222-2-222222222-20000-2-22222-2-200000000-2-2000000000000-2-222220000-200000000
χ272222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-222-2-2−1+52−1−521−521−521+521+52−1+52−1−522-22-2−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000−1+52−1−521−521+52000000000
χ282222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-222-2-2−1+52−1−521−521−521+521+52−1+52−1−52-22-221−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000001−521+52−1+52−1−52000000000
χ292222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-222−1+52−1−521−521−521+521+52−1+52−1−522-2-221−521−521+521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000−1+52−1−521−521+52000000000
χ302222-2-222−1+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+52−1+52−1−52-222-2−1+52−1+52−1−52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000001−521+52−1+52−1−52000000000
χ312222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-222-2-2−1−52−1+521+521+521−521−52−1−52−1+522-22-2−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000−1−52−1+521+521−52000000000
χ322222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-222-2-2−1−52−1+521+521+521−521−52−1−52−1+52-22-221+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000001+521−52−1−52−1+52000000000
χ332222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-222−1−52−1+521+521+521−521−52−1−52−1+522-2-221+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+52000000−1−52−1+521+521−52000000000
χ342222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-222−1−52−1+521+521+521−521−52−1−52−1+52-222-2−1−52−1−52−1+52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000001+521−52−1−52−1+52000000000
χ352222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000002200000000000022-2-2220000-200000000
χ362222-2-2-2-22222222220000-2-2-2-2-2-2-2-20000000022000000000000-2-222-2-20000200000000
χ3722-2-22-20022-2-2-2-22202−22−2002-22-200000000000000002−22−22−22−2002i−2i2i−2i00000i2−i2i2−i20000
χ3822-2-22-20022-2-2-2-22202−22−2002-22-200000000000000002−22−22−22−200−2i2i−2i2i00000−i2i2−i2i20000
χ3922-2-22-20022-2-2-2-2220−22−22002-22-20000000000000000−22−22−22−22002i−2i2i−2i00000−i2i2−i2i20000
χ4022-2-22-20022-2-2-2-2220−22−22002-22-20000000000000000−22−22−22−2200−2i2i−2i2i00000i2−i2i2−i20000
χ4122-2-2-220022-2-2-2-22202−2−2200-22-2200000000000000002−22−2−22−22002i−2i−2i2i00000i2−i2−i2i20000
χ4222-2-2-220022-2-2-2-22202−2−2200-22-2200000000000000002−22−2−22−2200−2i2i2i−2i00000−i2i2i2−i20000
χ4322-2-2-220022-2-2-2-2220−222−200-22-220000000000000000−22−222−22−2002i−2i−2i2i00000−i2i2i2−i20000
χ4422-2-2-220022-2-2-2-2220−222−200-22-220000000000000000−22−222−22−200−2i2i2i−2i00000i2−i2−i2i20000
χ45444444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-400001−51+5−1+5−1+5−1−5−1−51−51+5000000001−51+50000000000000000000000000000000
χ46444444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-400001+51−5−1−5−1−5−1+5−1+51+51−5000000001+51−50000000000000000000000000000000
χ474444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5400001−51+51−51−51+51+51−51+500000000−1+5−1−50000000000000000000000000000000
χ484444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5400001+51−51+51+51−51−51+51−500000000−1−5−1+50000000000000000000000000000000
χ4944-4-44-400−1+5−1−51−51−51+51+5−1+5−1−5022−2222−2200−1+51−5−1−51+50000000000000000−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+ζ390000000000000000000
χ5044-4-44-400−1+5−1−51−51−51+51+5−1+5−1−50−2222−222200−1+51−5−1−51+50000000000000000ζ7−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−ζ390000000000000000000
χ5144-4-44-400−1−5−1+51+51+51−51−5−1−5−1+5022−2222−2200−1−51+5−1+51−50000000000000000ζ21+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−ζ370000000000000000000
χ5244-4-44-400−1−5−1+51+51+51−51−5−1−5−1+50−2222−222200−1−51+5−1+51−50000000000000000−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+ζ370000000000000000000
χ5344-4-4-4400−1+5−1−51−51−51+51+5−1+5−1−5022−22−2222001−5−1+51+5−1−50000000000000000−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−ζ390000000000000000000
χ5444-4-4-4400−1+5−1−51−51−51+51+5−1+5−1−50−222222−22001−5−1+51+5−1−50000000000000000ζ7−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+ζ390000000000000000000
χ5544-4-4-4400−1−5−1+51+51+51−51−5−1−5−1+5022−22−2222001+5−1−51−5−1+50000000000000000ζ21+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+ζ370000000000000000000
χ5644-4-4-4400−1−5−1+51+51+51−51−5−1−5−1+50−222222−22001+5−1−51−5−1+50000000000000000−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−ζ370000000000000000000
χ574-44-4004-4444-44-4-4-400000440000-4-400000000000000000000000000000000000000000
χ584-44-4004-4−1+5−1−5−1+51−5−1−51+51−51+500000−1+5−1−500001−51+50000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000
χ594-44-4004-4−1+5−1−5−1+51−5−1−51+51−51+500000−1+5−1−500001−51+500000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000
χ604-44-4004-4−1−5−1+5−1−51+5−1+51−51+51−500000−1−5−1+500001+51−500000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000000
χ614-44-4004-4−1−5−1+5−1−51+5−1+51−51+51−500000−1−5−1+500001+51−50000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000000
χ624-44-400-44444-44-4-4-400000-4-400004400000000000000000000000000000000000000000
χ634-44-400-44−1+5−1−5−1+51−5−1−51+51−51+5000001−51+50000−1+5−1−500002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000000
χ644-44-400-44−1+5−1−5−1+51−5−1−51+51−51+5000001−51+50000−1+5−1−50000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000000
χ654-44-400-44−1−5−1+5−1−51+5−1+51−51+51−5000001+51−50000−1−5−1+50000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000000
χ664-44-400-44−1−5−1+5−1−51+5−1+51−51+51−5000001+51−50000−1−5−1+500002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000000
χ674-4-44000044-44-44-4-4000000000000000000000000000000000004-400000000000000000
χ684-4-44000044-44-44-4-400000000000000000000000000000000000-4400000000000000000
χ698-8-880000−2+25−2−252−25−2+252+25−2−252−252+25000000000000000000000000000000000000000000000000000000
χ708-8-880000−2−25−2+252+25−2−252−25−2+252+252−25000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.