Finite Group Databasebeta

← Group #12255809

Character table — Group #12255809

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101
size111122222222222222444444444444444444444488888888888888888888888888810101616161616161616161616202020202020202020323232324040404040808080
order1222445588881010101010104416161616202020202020202040404040404040402281616202040404040808080808080808080808080808080804444410101010202020202248816161616202020202281616244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1-1-1
χ41111111111111111111111111111111111111111-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ511111111111111111111-1-1-1-11111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111111111-1-1-1-1-1-1-1-1-1-11-1-11-11
χ611111111111111111111-1-1-1-11111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-11111-1-1-1-111-111-11-1
χ711111111111111111111-1-1-1-11111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-11-1
χ811111111111111111111-1-1-1-11111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-11
χ9111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11-11111-1-1-1-11-1-111111111-1-111-1-1-1-1-11
χ10111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111-1
χ11111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1-1-1-111111-1-1111111-1-111-1-1-1-1-111-1
χ12111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-111-1-1-1-1-1-1-1-11111111-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-111-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-111-1-11111-1-111111-1-11-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111111-1-111-1-1-1-111-1-111-1111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-11111-111-1-1111111-1-1-1-11-1-1-111
χ1722222222-2-2-2-222222222000022222222-2-2-2-2-2-2-2-200-20022-2-2-2-200000000000000002200000000000222-2-20000000000-200000
χ1822222222-2-2-2-222222222000022222222-2-2-2-2-2-2-2-200-20022-2-2-2-20000000000000000-2-200000000000-2-2-2220000000000200000
χ1922222222-2-2-2-2222222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-200200-2-22222000000000000000022000000000002-2-2-2-20000000000200000
χ2022222222-2-2-2-2222222-2-20000-2-2-2-22222-2-2-2-2-2-2-2-200200-2-222220000000000000000-2-200000000000-222220000000000-200000
χ21222222−1+52−1−522222−1+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+52−1−52−1−5222222−1+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+52−1−52−1−52−1−52−1−5200222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000−1+52−1−52−1+52−1−5200000000
χ22222222−1+52−1−522222−1+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+52−1−52−1−52-2-2222−1+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+52−1−52−1−52−1−52−1−5200-2-2-21−521−521+521+521−521−521+521+520000000001−521+521−521+5200000000
χ23222222−1+52−1−522222−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52222-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52002-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000001−521+521−521+5200000000
χ24222222−1+52−1−522222−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52-2-22-2-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200-2221−521−521+521+521−521−521+521+52000000000−1+52−1−52−1+52−1−5200000000
χ25222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-222221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-21−521+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+521+521+5200-22-2−1+52−1+52−1−52−1−521−521−521+521+52000000000−1+52−1−521−521+5200000000
χ26222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-222221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-21−521+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+521+521+52002-221−521−521+521+52−1+52−1+52−1−52−1−520000000001−521+52−1+52−1−5200000000
χ27222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2221−521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-22−1+52−1+52−1−52−1−521−521−521+521+520000000001−521+52−1+52−1−5200000000
χ28222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2221−521+521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520022-21−521−521+521+52−1+52−1+52−1−52−1−52000000000−1+52−1−521−521+5200000000
χ29222222−1−52−1+522222−1−52−1+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+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+5200222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000−1−52−1+52−1−52−1+5200000000
χ30222222−1−52−1+522222−1−52−1+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+52-2-2222−1−52−1+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+5200-2-2-21+521+521−521−521+521+521−521−520000000001+521−521+521−5200000000
χ31222222−1−52−1+522222−1−52−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222-2-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52002-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000001+521−521+521−5200000000
χ32222222−1−52−1+522222−1−52−1+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+52−1−52−1−52−1+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+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200-2221+521+521−521−521+521+521−521−52000000000−1−52−1+52−1−52−1+5200000000
χ33222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-222221+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+5222-2-2-21+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+521−521−521−521−5200-22-2−1−52−1−52−1+52−1+521+521+521−521−52000000000−1−52−1+521+521−5200000000
χ34222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-222221+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+52-2-2-2-2-21+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+521−521−521−521−52002-221+521+521−521−52−1−52−1−52−1+52−1+520000000001+521−52−1−52−1+5200000000
χ35222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-21+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+5222-2221+521−521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-22−1−52−1−52−1+52−1+521+521+521−521−520000000001+521−52−1−52−1+5200000000
χ36222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-21+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+52-2-2-2221+521−521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520022-21+521+521−521−52−1−52−1−52−1+52−1+52000000000−1−52−1+521+521−5200000000
χ372222-2-22200002222222-222−2−22222-2-2-2-2000000000002−2-2-2000022−2−222−2−222−2−222−2−22200000000000-22-20022−2−200000002−2000
χ382222-2-22200002222222-222−2−22222-2-2-2-2000000000002−2-2-2000022−2−222−2−222−2−222−2−2-2-2000000000002-2200−2−2220000000−22000
χ392222-2-22200002222222-2−2−2222222-2-2-2-200000000000−22-2-20000−2−222−2−222−2−222−2−2222200000000000-22-200−2−2220000000−22000
χ402222-2-22200002222222-2−2−2222222-2-2-2-200000000000−22-2-20000−2−222−2−222−2−222−2−222-2-2000000000002-220022−2−200000002−2000
χ412222-2-2220000222222-2222−2−2-2-2-2-2-2-2-2-200000000000−2222000022−2−222−2−2−2−222−2−2222200000000000-2-220022−2−20000000−22000
χ422222-2-2220000222222-2222−2−2-2-2-2-2-2-2-2-200000000000−2222000022−2−222−2−2−2−222−2−222-2-20000000000022-200−2−22200000002−2000
χ432222-2-2220000222222-22−2−222-2-2-2-2-2-2-2-2000000000002−2220000−2−222−2−22222−2−222−2−22200000000000-2-2200−2−22200000002−2000
χ442222-2-2220000222222-22−2−222-2-2-2-2-2-2-2-2000000000002−2220000−2−222−2−22222−2−222−2−2-2-20000000000022-20022−2−20000000−22000
χ452-2-22-2222-2-222-2-2-2-22200000000002-22-2-2-2-2-222222-20000000000000000000000000000002-22-20000000002-22-200002-2000000
χ462-2-22-2222-2-222-2-2-2-22200000000002-22-2-2-2-2-222222-20000000000000000000000000000002-22-2000000000-22-220000-22000000
χ472-2-22-2222-2-222-2-2-2-22200000000002-22-2-2-2-2-22222-22000000000000000000000000000000-22-220000000002-22-20000-22000000
χ482-2-22-2222-2-222-2-2-2-22200000000002-22-2-2-2-2-22222-22000000000000000000000000000000-22-22000000000-22-2200002-2000000
χ49444444−1+5−1−5-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5440000−1+5−1+5−1−5−1−5−1+5−1+5−1−5−1−51−51−51+51+51−51−51+51+500-400−1+5−1−51−51−51+51+500000000000000000000000000000000000000000000000000
χ50444444−1+5−1−5-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5-4-400001−51−51+51+5−1+5−1+5−1−5−1−51−51−51+51+51−51−51+51+5004001−51+5−1+5−1+5−1−5−1−500000000000000000000000000000000000000000000000000
χ51444444−1−5−1+5-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5440000−1−5−1−5−1+5−1+5−1−5−1−5−1+5−1+51+51+51−51−51+51+51−51−500-400−1−5−1+51+51+51−51−500000000000000000000000000000000000000000000000000
χ52444444−1−5−1+5-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5-4-400001+51+51−51−5−1−5−1−5−1+5−1+51+51+51−51−51+51+51−51−5004001+51−5−1−5−1−5−1+5−1+500000000000000000000000000000000000000000000000000
χ534444-4-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−54-42222−22−22−1+5−1+5−1−5−1−51−51−51+51+50000000000022−221−51+50000−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ78−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ780000000000000000000000000000000000
χ544444-4-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−54-4−22−222222−1+5−1+5−1−5−1−51−51−51+51+500000000000−22221−51+50000ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ78ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ780000000000000000000000000000000000
χ554444-4-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−5-442222−22−221−51−51+51+51−51−51+51+500000000000−2222−1+5−1−50000−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ78−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ78ζ14−ζ26+ζ46−ζ74ζ14−ζ26+ζ46−ζ74−ζ14+ζ26−ζ46+ζ74−ζ14+ζ26−ζ46+ζ74−ζ42−ζ58+ζ62+ζ78−ζ42−ζ58+ζ62+ζ78ζ42+ζ58−ζ62−ζ78ζ42+ζ58−ζ62−ζ780000000000000000000000000000000000
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χ814-44-4004422−22−222244-4-4-4-40000000000000022−2222−22−2222−22220000000000000000000000000004i−4i000000000000002i2−2i20000000000000000
χ824-44-4004422−22−222244-4-4-4-40000000000000022−2222−22−2222−2222000000000000000000000000000−4i4i00000000000000−2i22i20000000000000000
χ834-44-40044−222222−2244-4-4-4-400000000000000−2222−222222−2222−220000000000000000000000000004i−4i00000000000000−2i22i20000000000000000
χ844-44-40044−222222−2244-4-4-4-400000000000000−2222−222222−2222−22000000000000000000000000000−4i4i000000000000002i2−2i20000000000000000
χ854-4-444-4440000-4-4-4-4440000000000-44-440000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ864-4-444-4440000-4-4-4-4440000000000-44-4400000000000000000000000000000000000000000000000000000−222222−22000000000000
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χ988-88-800−2−25−2+2542−42−4242−2−25−2+252+252−252+252−25000000000000002ζ42+2ζ58−2ζ62−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26+2ζ46−2ζ74−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ740000000000000000000000000000000000000000000000000000000000000
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χ1008-8-888-8−2+25−2−2500002−252+252−252+25−2+25−2−2500000000002−25−2+252+25−2−25000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-888-8−2−25−2+2500002+252−252+252−25−2−25−2+2500000000002+25−2−252−25−2+25000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.