Finite Group Databasebeta

← Group #12253547

Character table — Group #12253547

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146
size1111222222222222222244444444444444444444444444444441616161616161616161620202020202020204040404011112222222222222222444444444444444444444444444444416161616161616161616202020202020202040404040
order12224444558888101010101010488202020202020202020202020404040404040404040404040404040404420202020202020201616161616161616444422224444101088881010101010104882020202020202020202020204040404040404040404040404040404044202020202020202016161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-11111-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-11111-1-111
χ71111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111
χ81111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1
χ92222222222-2-2-2-22222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000002222222222-2-2-2-22222222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000
χ1022222222−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000022222222−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ1122222222−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+5200000000000022222222−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+52000000000000
χ1222222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ7200000000000022222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000000000
χ1322222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ7200000000000022222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5200−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000000000
χ1422222222−1−52−1+522222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000022222222−1−52−1+522222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ1522222222−1−52−1+522222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−5200000000000022222222−1−52−1+522222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−52000000000000
χ1622222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ5600000000000022222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000000000
χ1722222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ5600000000000022222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5200ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000000000
χ18222222-2-2220000222222-20022-2-222-2-2-2-2-2-20000000000000000000000000022−2−222−2−20000222222-2-2220000222222-20022-2-222-2-2-2-2-2-20000000000000000000000000022−2−222−2−20000
χ19222222-2-2220000222222-20022-2-222-2-2-2-2-2-200000000000000000000000000−2−222−2−2220000222222-2-2220000222222-20022-2-222-2-2-2-2-2-200000000000000000000000000−2−222−2−2220000
χ202222-2-22222-2-2-2-2222222-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000002222-2-22222-2-2-2-2222222-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000
χ212222-2-222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-2−1+52−1+52−1−52−1−521−521−521+521+520000000000002222-2-222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522-2−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ222222-2-222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−520000000000002222-2-222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-21−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-221−521−521+521+52−1+52−1+52−1−52−1−52000000000000
χ232222-2-222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52-2221−521−521−521−521+521+521+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+52−1−52−1−52−1−52−1−5200ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ720000000000002222-2-222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52-2221−521−521−521−521+521+521+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+52−1−52−1−52−1−52−1−5200ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72000000000000
χ242222-2-222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52-2221−521−521−521−521+521+521+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+52−1−52−1−52−1−52−1−5200−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ720000000000002222-2-222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52-2221−521−521−521−521+521+521+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+52−1−52−1−52−1−52−1−5200−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72000000000000
χ252222-2-222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-21+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+52−1+52−1+521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+521+521+521−521−520000000000002222-2-222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-21+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+52−1+52−1+521+521+521+521+521−521−521−521−522-2−1−52−1−52−1+52−1+521+521+521−521−52000000000000
χ262222-2-222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-21+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+52−1+52−1+521+521+521+521+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+520000000000002222-2-222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-21+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+52−1+52−1+521+521+521+521+521−521−521−521−52-221+521+521−521−52−1−52−1−52−1+52−1+52000000000000
χ272222-2-222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52-2221+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ560000000000002222-2-222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52-2221+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56000000000000
χ282222-2-222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52-2221+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ560000000000002222-2-222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52-2221+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56000000000000
χ292222-2-2-2-2220000222222200-2-222-2-222-2-2-2-20000000000000000000000000022−2−2−2−22200002222-2-2-2-2220000222222200-2-222-2-222-2-2-2-20000000000000000000000000022−2−2−2−2220000
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χ1464-4-4400-44−1−5−1+500001+51+51−51−5−1−5−1+5000000000001+5−1−51−5−1+5000000002ζ8−2ζ72−2ζ8+2ζ72−2ζ8+2ζ722ζ8−2ζ72−2ζ24+2ζ562ζ24−2ζ562ζ24−2ζ56−2ζ24+2ζ560000000000000000000000-444-4004-41+51−50000−1−5−1−5−1+5−1+51+51−500000000000−1−51+5−1+51−500000000−2ζ8+2ζ722ζ8−2ζ722ζ8−2ζ72−2ζ8+2ζ722ζ24−2ζ56−2ζ24+2ζ56−2ζ24+2ζ562ζ24−2ζ560000000000000000000000

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