Finite Group Databasebeta

← Group #10612764

Character table — Group #10612764

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size111122222222222244444444444888888888888888888888881616161620202020202020202020404040
order1222444455101010101010444202020202020202044488202020202020202020204040404040404040202020202244448888444
χ11111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111
χ4111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ511111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1
χ611111111111111111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-111
χ711111111111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1
χ811111111111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ91111-1-11111111111-11111-1-1-1-1111-1-11-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-111-1-111-11-1
χ101111-1-11111111111-11111-1-1-1-1111-1-11-1-1-11111-1-1-1-11111-1-1-1-111-1-1-11-11-1-111-1-11-11
χ111111-1-11111111111-11111-1-1-1-111-11-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1111-11-1-1-111-1-111-1
χ121111-1-11111111111-11111-1-1-1-111-11-1-11-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1111-1-111-1-11
χ131111-1-11111111111-1-1-111-1-1-1-1111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-11111-1-1-1-11
χ141111-1-11111111111-1-1-111-1-1-1-1111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-1-1-1-11111-1
χ151111-1-11111111111-1-1-111-1-1-1-111-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-1-1-1-1111-11
χ161111-1-11111111111-1-1-111-1-1-1-111-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-111111-1-1-11-1
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
χ25222222-2-222222222-200-2-22222-2-200000-2-20000000000000000000022-2-2000000000
χ26222222-2-222222222-200-2-22222-2-200000-2-200000000000000000000-2-222000000000
χ272222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-222−1+52−1−521−521−521+521+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+52−1−52-222−1+52−1−521−521−521+521+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+52−1−52-2-2-2−1+52−1−521−521−521+521+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+52−1−52-2-2-2−1+52−1−521−521−521+521+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+52-222−1−52−1+521+521+521−521−52−1−52−1+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+52-222−1−52−1+521+521+521−521−52−1−52−1+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+52-2-2-2−1−52−1+521+521+521−521−52−1−52−1+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+52-2-2-2−1−52−1+521+521+521−521−52−1−52−1+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
χ352222-2-2-2-222222222200-2-2-2-2-2-2-2-20000022000000000000000000002-2-22000000000
χ362222-2-2-2-222222222200-2-2-2-2-2-2-2-2000002200000000000000000000-222-2000000000
χ372-22-200-22222-22-2-2-202i−2i-2-200002200000002i−2i2i−2i000000000000000000002i−2i002-2000
χ382-22-200-22222-22-2-2-202i−2i-2-200002200000002i−2i2i−2i00000000000000000000−2i2i00-22000
χ392-22-200-22222-22-2-2-20−2i2i-2-20000220000000−2i2i−2i2i000000000000000000002i−2i00-22000
χ402-22-200-22222-22-2-2-20−2i2i-2-20000220000000−2i2i−2i2i00000000000000000000−2i2i002-2000
χ41444444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4001−51+5−1+5−1+5−1−5−1−51−51+5000001−51+5000000000000000000000000000000000
χ42444444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4001+51−5−1−5−1−5−1+5−1+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
χ4544-4-44-40044-4-4-4-444000004-44-4000000000000000000000000000000000000000000
χ4644-4-44-400−1+5−1−51−51−51+51+5−1+5−1−500000−1+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−ζ3900000000000000000
χ4744-4-44-400−1+5−1−51−51−51+51+5−1+5−1−500000−1+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+ζ3900000000000000000
χ4844-4-44-400−1−5−1+51+51+51−51−5−1−5−1+500000−1−51+5−1+51−500000000000000000−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
χ4944-4-44-400−1−5−1+51+51+51−51−5−1−5−1+500000−1−51+5−1+51−500000000000000000ζ21−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
χ5044-4-4-440044-4-4-4-44400000-44-44000000000000000000000000000000000000000000
χ5144-4-4-4400−1+5−1−51−51−51+51+5−1+5−1−5000001−5−1+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+ζ3900000000000000000
χ5244-4-4-4400−1+5−1−51−51−51+51+5−1+5−1−5000001−5−1+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−ζ3900000000000000000
χ5344-4-4-4400−1−5−1+51+51+51−51−5−1−5−1+5000001+5−1−51−5−1+500000000000000000−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
χ5444-4-4-4400−1−5−1+51+51+51−51−5−1−5−1+5000001+5−1−51−5−1+500000000000000000ζ21−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
χ554-44-4004-4444-44-4-4-4000440000-4-40000000000000000000000000000000000000000
χ564-44-4004-4−1+5−1−5−1+51−5−1−51+51−51+5000−1+5−1−500001−51+5000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000
χ574-44-4004-4−1+5−1−5−1+51−5−1−51+51−51+5000−1+5−1−500001−51+500000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000
χ584-44-4004-4−1−5−1+5−1−51+5−1+51−51+51−5000−1−5−1+500001+51−500000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000
χ594-44-4004-4−1−5−1+5−1−51+5−1+51−51+51−5000−1−5−1+500001+51−5000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000
χ604-44-400-44−1+5−1−5−1+51−5−1−51+51−51+504i−4i1−51+50000−1+5−1−50000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400000000000000000000000000000
χ614-44-400-44−1+5−1−5−1+51−5−1−51+51−51+50−4i4i1−51+50000−1+5−1−500000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400000000000000000000000000000
χ624-44-400-44−1−5−1+5−1−51+5−1+51−51+51−504i−4i1+51−50000−1−5−1+50000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ3800000000000000000000000000000
χ634-44-400-44−1−5−1+5−1−51+5−1+51−51+51−50−4i4i1+51−50000−1−5−1+500000002ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ3800000000000000000000000000000
χ644-4-44000044-44-44-4-4000000000000000000000000000000000000000000002i2−2i200000
χ654-4-44000044-44-44-4-400000000000000000000000000000000000000000000−2i22i200000
χ668-8-880000−2+25−2−252−25−2+252+25−2−252−252+25000000000000000000000000000000000000000000000000000
χ678-8-880000−2−25−2+252+25−2−252−25−2+252+252−25000000000000000000000000000000000000000000000000000

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