Finite Group Databasebeta

← Group #12256272

Character table — Group #12256272

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107
size11112222222222222244444444444444444444444444888888888888888888888888888101016161616161616161616161616161616161620202020202020202040404080808080
order1222445588881010101010102410101010161616162020202020202020404040404040404022448161640404040808080808080808080808080808080802244101010102020202020202020202020204448816161616816162244
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111111111-1-1-1-1-1-1-1-111111-1-1-1-11-1-11-11-1
χ6111111111111111111111111-1-1-1-1111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11-11
χ7111111111111111111111111-1-1-1-11111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-11111111111111-1-1-1-11-1-1-11-11
χ8111111111111111111111111-1-1-1-11111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1111-11-1
χ9111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1111111-1-1-11-1-11
χ10111111111111111111-1-1-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1111-111-1
χ11111111111111111111-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1111111-1-1-1-111-1
χ12111111111111111111-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-11111-1-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-11111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111111-1-1-1-1-1-1-1-11111-111-1-111111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111111111-1-1-1-11-1-111-1-1-1-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-111111111-1-1-1-1-111-1-111111-1-111-1-1
χ1722222222-2-2-2-2222222222222000022222222-2-2-2-2-2-2-2-20000-200-2-2-2-2000000000000000022000000000000000000222-2-20000-2000000
χ1822222222-2-2-2-2222222222222000022222222-2-2-2-2-2-2-2-20000-200-2-2-2-20000000000000000-2-2000000000000000000-2-2-22200002000000
χ1922222222-2-2-2-2222222-2-2-2-2-2-2000022-2-2-2-222-2-2-2-2-2-2-2-2000020022220000000000000000220000000000000000002-2-2-2-200002000000
χ2022222222-2-2-2-2222222-2-2-2-2-2-2000022-2-2-2-222-2-2-2-2-2-2-2-2000020022220000000000000000-2-2000000000000000000-222220000-2000000
χ21222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−522222222−1+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+52−1−52−1−52−1−52−1−520022−1+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+52−1−52−1−520000000000000000
χ22222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−52-2-2-2-2222−1+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+52−1−52−1−52−1−52−1−5200-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ23222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52-2-2-2-2−1+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+52−1−52−1−5222-2-22-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52002-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ24222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52-2-2-2-2−1+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+52−1−52−1−52-2-2222-2-2−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ25222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-21−521−521+521+522222−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222-2-2-21−521−521+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+5200-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ26222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-21−521−521+521+522222−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-2-21−521−521+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+5200221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ27222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-21−521−521+521+52-2-2-2-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-2221−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
χ28222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-21−521−521+521+52-2-2-2-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222-2221−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ29222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+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+522222222−1−52−1−52−1+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+520022−1−52−1−52−1+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+520000000000000000
χ30222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+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+52-2-2-2-2222−1−52−1−52−1+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+5200-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ31222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+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+5222-2-22-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52002-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ32222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+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+52-2-2222-2-2−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ33222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-21+521+521−521−522222−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222-2-2-21+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ34222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-21+521+521−521−522222−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-2-21+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−5200221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ35222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-21+521+521−521−52-2-2-2-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2-2221+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+5200-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000
χ36222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-21+521+521−521−52-2-2-2-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222-2221+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+52002-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000
χ372222-2-22200002222222-2222222−2−2-2-2-2-2-2-2-2-200000000000002−2000022−2−222−2−222−2−222−2−222000000000000000000-2-220022−2−202−20000
χ382222-2-22200002222222-2222222−2−2-2-2-2-2-2-2-2-200000000000002−2000022−2−222−2−222−2−222−2−2-2-200000000000000000022-200−2−2220−220000
χ392222-2-22200002222222-22222−2−222-2-2-2-2-2-2-2-20000000000000−220000−2−222−2−222−2−222−2−22222000000000000000000-2-2200−2−2220−220000
χ402222-2-22200002222222-22222−2−222-2-2-2-2-2-2-2-20000000000000−220000−2−222−2−222−2−222−2−222-2-200000000000000000022-20022−2−202−20000
χ412222-2-2220000222222-22-2-2-2-222−2−2-2-22222-2-20000000000000−22000022−2−222−2−2−2−222−2−22222000000000000000000-22-20022−2−20−220000
χ422222-2-2220000222222-22-2-2-2-222−2−2-2-22222-2-20000000000000−22000022−2−222−2−2−2−222−2−222-2-20000000000000000002-2200−2−22202−20000
χ432222-2-2220000222222-22-2-2-2-2−2−222-2-22222-2-200000000000002−20000−2−222−2−22222−2−222−2−222000000000000000000-22-200−2−22202−20000
χ442222-2-2220000222222-22-2-2-2-2−2−222-2-22222-2-200000000000002−20000−2−222−2−22222−2−222−2−2-2-20000000000000000002-220022−2−20−220000
χ4522-2-2-222222-2-2-2-222-2-20000002i−2i2i−2i-2-20000222222-2-2-2-22-22i−2i00000002i−2i2i−2i2i−2i2i−2i0000000000002-22-200002i−2i2i−2i00000000000000000000
χ4622-2-2-222222-2-2-2-222-2-20000002i−2i2i−2i-2-20000222222-2-2-2-2-22−2i2i00000002i−2i2i−2i2i−2i2i−2i000000000000-22-220000−2i2i−2i2i00000000000000000000
χ4722-2-2-222222-2-2-2-222-2-2000000−2i2i−2i2i-2-20000222222-2-2-2-22-2−2i2i0000000−2i2i−2i2i−2i2i−2i2i0000000000002-22-20000−2i2i−2i2i00000000000000000000
χ4822-2-2-222222-2-2-2-222-2-2000000−2i2i−2i2i-2-20000222222-2-2-2-2-222i−2i0000000−2i2i−2i2i−2i2i−2i2i000000000000-22-2200002i−2i2i−2i00000000000000000000
χ4922-2-2-22−1+52−1−5222-2-21−521+52−1+52−1−521−521+5200ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ722i−2i2i−2i1−521+52ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+522-22i−2i000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ44−ζ76ζ44+ζ76−ζ44−ζ76ζ44+ζ76−ζ12−ζ28ζ12+ζ28−ζ12−ζ28ζ12+ζ28−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ280000−1+521−52−1−521+52ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ44−ζ76ζ44+ζ76−ζ12−ζ28ζ12+ζ28−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ280000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.