Finite Group Databasebeta

← Group #12090320

Character table — Group #12090320

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222224444444444444888888888888888888888888161616161616161616161616161616161616162020202020202020323240404040404040408080
order1222444455101010101010444442020202020202020248888202020202020202020204040404040404040228101010101010202040404040404040404488888810102448888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-11111-1
χ41111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-11
χ5111111111111111111-1-11111111111-111111111-1-1-1-11111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-11-1-1111-1-1-1-1
χ6111111111111111111-1-11111111111-111111111-1-1-1-11111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111
χ7111111111111111111-1-11111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11-1-1-11
χ8111111111111111111-1-11111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-1111-1
χ91111111111111111-1-111111111111-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111111-1-1-1-1-11-1
χ101111111111111111-1-111111111111-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-111111-11
χ111111111111111111-1-111111111111-11-1-111-1-1-1-111111111111111-1-11-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-111
χ121111111111111111-1-111111111111-11-1-111-1-1-1-111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-111-1-1111-1-1
χ131111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-11111-1-11111111111-1-11111-1-11-1-1-1-1-111-11
χ141111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-11111-1-111111111-1-111-1-1-1-1-1-1-111111-1-11-1
χ151111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-111-1-1
χ161111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111
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+52−1−52222222−1+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+52−1−52−1−52−1−52−1−52222−1+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+52−1−52−1−5200000000−1+52−1−520000000000
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+52−1−5222-2-2-2-2−1+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+522-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+52000000001−521+520000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-22222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+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+52−1+52−1+52−1−52−1−521−521−521+521+52000000001−521+520000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52-222−1+52−1−521−521−521+521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000−1+52−1−520000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2222-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-22-21−521+521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200000000−1+52−1−520000000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-22-2-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-221−521+521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000001−521+520000000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222-2-21−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+522-221−521+52−1+52−1+52−1−52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000001−521+520000000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+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+521−521−521+521+5200000000−1+52−1−520000000000
χ2522222222−1−52−1+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+52222222−1−52−1−52−1+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+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+5200000000−1−52−1+520000000000
χ2622222222−1−52−1+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+5222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000000001+521−520000000000
χ2722222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-22222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2-2−1−52−1+521+521+521−521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52000000001+521−520000000000
χ2822222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52-222−1−52−1+521+521+521−521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000−1−52−1+520000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2222-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-22-21+521−521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200000000−1−52−1+520000000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-22-2-2221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-221+521−521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000001+521−520000000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-222-2-21+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−522-221+521−52−1−52−1−52−1+52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000001+521−520000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2221+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+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+521−521−5200000000−1−52−1+520000000000
χ3322222-2-22222222222200-222-2-222-2-2-20000022220000-2-200000000000-2-2000000000000002222000000-20000-20000
χ3422222-2-22222222222200-222-2-222-2-2-20000022220000-2-200000000000-2-200000000000000-2-2-2-20000002000020000
χ3522222-2-2222222222-2-200-222-2-222-2-2200000-2-2-2-20000-2-200000000000220000000000000022-2-2000000-2000020000
χ3622222-2-2222222222-2-200-222-2-222-2-2200000-2-2-2-20000-2-2000000000002200000000000000-2-22200000020000-20000
χ372222-222-2222222220022-2-2-222-2-2220-2000000002222-2-200000000000000000-2-200000000000022-2-2000-220000000
χ382222-222-2222222220022-2-2-222-2-2220-2000000002222-2-200000000000000000-2-2000000000000-2-2220002-20000000
χ392222-222-22222222200-2-2-2-2-222-2-2220200000000-2-2-2-2-2-2000000000000000002200000000000022-2-20002-20000000
χ402222-222-22222222200-2-2-2-2-222-2-2220200000000-2-2-2-2-2-20000000000000000022000000000000-2-222000-220000000
χ412-22-2200-22222-2-2-2-22i−2i0002200-2-20000i2−i22−22i−2i2i−2i00000022−2−222−2−200000000000i2−i2i2−i200002i−2i2-22−22−200000i2−i200000
χ422-22-2200-22222-2-2-2-22i−2i0002200-2-20000i2−i22−22i−2i2i−2i00000022−2−222−2−200000000000i2−i2i2−i20000−2i2i-22−22−2200000−i2i200000
χ432-22-2200-22222-2-2-2-22i−2i0002200-2-20000−i2i2−222i−2i2i−2i000000−2−222−2−22200000000000−i2i2−i2i200002i−2i2-2−22−2200000−i2i200000
χ442-22-2200-22222-2-2-2-22i−2i0002200-2-20000−i2i2−222i−2i2i−2i000000−2−222−2−22200000000000−i2i2−i2i20000−2i2i-222−22−200000i2−i200000
χ452-22-2200-22222-2-2-2-2−2i2i0002200-2-20000i2−i2−22−2i2i−2i2i000000−2−222−2−22200000000000i2−i2i2−i200002i−2i-222−22−200000−i2i200000
χ462-22-2200-22222-2-2-2-2−2i2i0002200-2-20000i2−i2−22−2i2i−2i2i000000−2−222−2−22200000000000i2−i2i2−i20000−2i2i2-2−22−2200000i2−i200000
χ472-22-2200-22222-2-2-2-2−2i2i0002200-2-20000−i2i22−2−2i2i−2i2i00000022−2−222−2−200000000000−i2i2−i2i200002i−2i-22−22−2200000i2−i200000
χ482-22-2200-22222-2-2-2-2−2i2i0002200-2-20000−i2i22−2−2i2i−2i2i00000022−2−222−2−200000000000−i2i2−i2i20000−2i2i2-22−22−200000−i2i200000
χ4944444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54400-4−1+5−1−51−51+5−1+5−1−51−51+5-400000−1+5−1+5−1−5−1−500001−51+5000000000001−51+50000000000000000000000000000000000
χ5044444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-400-4−1+5−1−51−51+5−1+5−1−51−51+54000001−51−51+51+500001−51+500000000000−1+5−1−50000000000000000000000000000000000
χ5144444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54400-4−1−5−1+51+51−5−1−5−1+51+51−5-400000−1−5−1−5−1+5−1+500001+51−5000000000001+51−50000000000000000000000000000000000
χ5244444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-400-4−1−5−1+51+51−5−1−5−1+51+51−54000001+51+51−51−500001+51−500000000000−1−5−1+50000000000000000000000000000000000
χ534444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−50044-41−51+5−1+5−1−51−51+5−1+5−1−50-400000000−1+5−1+5−1−5−1−51−51+5000000000000000001−51+50000000000000000000000000000
χ544444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4-4-41−51+5−1+5−1−51−51+5−1+5−1−504000000001−51−51+51+51−51+500000000000000000−1+5−1−50000000000000000000000000000
χ554444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+50044-41+51−5−1−5−1+51+51−5−1−5−1+50-400000000−1−5−1−5−1+5−1+51+51−5000000000000000001+51−50000000000000000000000000000
χ564444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4-4-41+51−5−1−5−1+51+51−5−1−5−1+504000000001+51+51−51−51+51−500000000000000000−1−5−1+50000000000000000000000000000
χ574444-4-4-4-44444444400004-4-4-4-4-4-4-4-4000000000000004400000000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5000041−51+51−51+51−51+51−51+500000000000000−1+5−1−500000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000
χ594444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5000041−51+51−51+51−51+51−51+500000000000000−1+5−1−50000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000
χ604444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5000041+51−51+51−51+51−51+51−500000000000000−1−5−1+50000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000
χ614444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5000041+51−51+51−51+51−51+51−500000000000000−1−5−1+500000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000
χ624-44-4400-4−1+5−1−5−1+5−1−51−51+51−51+54i−4i000−1+5−1−5001−51+500002i2−2i222−22−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ3900000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39000000000000000000000000
χ634-44-4400-4−1+5−1−5−1+5−1−51−51+51−51+54i−4i000−1+5−1−5001−51+50000−2i22i2−2222−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ3900000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39000000000000000000000000
χ644-44-4400-4−1+5−1−5−1+5−1−51−51+51−51+5−4i4i000−1+5−1−5001−51+500002i2−2i2−22222ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ3900000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39000000000000000000000000
χ654-44-4400-4−1+5−1−5−1+5−1−51−51+51−51+5−4i4i000−1+5−1−5001−51+50000−2i22i222−222ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ3900000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39000000000000000000000000
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χ918-8-880-880−2+25−2−252−252+252−252+25−2+25−2−250000000−2+25−2−25002−252+25000000000000000000000000000000000000000000000000000000000000000
χ928-8-880-880−2−25−2+252+252−252+252−25−2−25−2+250000000−2−25−2+25002+252−25000000000000000000000000000000000000000000000000000000000000000

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