Finite Group Databasebeta

← Group #10612080

Character table — Group #10612080

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size111122222222222244444444444888888888888888888888881616161620202020202020202020404040
order1222444455101010101010224202020202020202022488101010102020202020204040404040404040101010102244448888224
χ11111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1
χ4111111111111111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
χ61111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1
χ71111111111111111-1-1111111111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1
χ81111111111111111-1-1111111111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ91111-1-1111111111111-111-1-1-1-1111-1-11-11111-1-1-1-1-1-11111-1-1-1-111-1-11-11-111-1-1111-1-1
χ101111-1-1111111111111-111-1-1-1-1111-1-11-11111-1-1-1-1-1-11111-1-1-1-111-1-1-11-11-1-111-1-1-111
χ111111-1-1111111111111-111-1-1-1-111-11-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1-1-111-1-11-11
χ121111-1-1111111111111-111-1-1-1-111-11-1-111111-1-1-1-1-1-1-1-1-1-11111-1-111-11-1111-1-111-11-1
χ131111-1-11111111111-1-1-111-1-1-1-1111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-11111-1-1-11-1
χ141111-1-11111111111-1-1-111-1-1-1-1111-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-1-1-1-1111-11
χ151111-1-11111111111-1-1-111-1-1-1-111-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-1-1-1-111-111
χ161111-1-11111111111-1-1-111-1-1-1-111-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-111111-1-11-1-1
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+52−1−52-2-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-21−521−521+521+52−1+52−1−521−521−521+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+52−1−52-2-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2221−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+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+52-2-22−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-21+521+521−521−52−1−52−1+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+52-2-22−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2221+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+521+521−521+521−520000000000000
χ25222222-2-22222222200-2-2-22222-2-2000000000-2-2000000000000000022-2-2000000000
χ26222222-2-22222222200-2-2-22222-2-2000000000-2-20000000000000000-2-222000000000
χ272222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2−1+52−1−521−521−521+521+52−1+52−1−522-2-22-2−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+520000000000000
χ282222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2−1+52−1−521−521−521+521+52−1+52−1−52-22-2-22−1+52−1+52−1−52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+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+5222-2−1−52−1+521+521+521−521−52−1−52−1+522-2-22-2−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−520000000000000
χ322222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2−1−52−1+521+521+521−521−52−1−52−1+52-22-2-22−1−52−1−52−1+52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+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
χ352222-2-2-2-222222222002-2-2-2-2-2-2-2-20000000002200000000000000002-2-22000000000
χ362222-2-2-2-222222222002-2-2-2-2-2-2-2-2000000000220000000000000000-222-2000000000
χ372-2-2200-22222-22-2-2-22-20-2-2000022000002-22-200000000000000000000002-2002-2000
χ382-2-2200-22222-22-2-2-22-20-2-2000022000002-22-20000000000000000000000-2200-22000
χ392-2-2200-22222-22-2-2-2-220-2-200002200000-22-2200000000000000000000002-200-22000
χ402-2-2200-22222-22-2-2-2-220-2-200002200000-22-220000000000000000000000-22002-2000
χ41444444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−500-41−51+5−1+5−1+5−1−5−1−51−51+50000000001−51+500000000000000000000000000000
χ42444444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-41+51−5−1−5−1−5−1+5−1+51+51−50000000001+51−500000000000000000000000000000
χ434444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−50041−51+51−51−51+51+51−51+5000000000−1+5−1−500000000000000000000000000000
χ444444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+50041+51−51+51+51−51−51+51−5000000000−1−5−1+500000000000000000000000000000
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+500000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+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+500000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−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+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−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−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+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+5−1−500000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−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+5−1−500000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+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+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+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−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ3700000000000000000
χ554-44-4000044-44-44-4-40000000000000000000000000000000000000000000022−2200000
χ564-44-4000044-44-44-4-400000000000000000000000000000000000000000000−222200000
χ574-4-44004-4444-44-4-4-4000440000-4-40000000000000000000000000000000000000000
χ584-4-44004-4−1+5−1−5−1+51−5−1−51+51−51+5000−1+5−1−500001−51+500000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000
χ594-4-44004-4−1+5−1−5−1+51−5−1−51+51−51+5000−1+5−1−500001−51+5000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000
χ604-4-44004-4−1−5−1+5−1−51+5−1+51−51+51−5000−1−5−1+500001+51−5000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000000000
χ614-4-44004-4−1−5−1+5−1−51+5−1+51−51+51−5000−1−5−1+500001+51−500000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000000000
χ624-4-4400-44−1+5−1−5−1+51−5−1−51+51−51+54-401−51+50000−1+5−1−500000−1+51−5−1−51+50000000000000000000000000000000
χ634-4-4400-44−1+5−1−5−1+51−5−1−51+51−51+5-4401−51+50000−1+5−1−5000001−5−1+51+5−1−50000000000000000000000000000000
χ644-4-4400-44−1−5−1+5−1−51+5−1+51−51+51−54-401+51−50000−1−5−1+500000−1−51+5−1+51−50000000000000000000000000000000
χ654-4-4400-44−1−5−1+5−1−51+5−1+51−51+51−5-4401+51−50000−1−5−1+5000001+5−1−51−5−1+50000000000000000000000000000000
χ668-88-80000−2+25−2−252−25−2+252+25−2−252−252+25000000000000000000000000000000000000000000000000000
χ678-88-80000−2−25−2+252+25−2−252−25−2+252+252−25000000000000000000000000000000000000000000000000000

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