Finite Group Databasebeta

← Group #72246552

Character table — Group #72246552

Order 7056.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11226666666612121212121212121212121212121212121212121414144242424242424249494949989898989898989898981261262942942942942941122666666661212121212121212121212121212121212121212141414424242424242424949494998989898989898989898126126294294294294294
order12367714142121424277714141421212121212121424242424242424121222828848484843366336612121212121214142666622661414141442424242141414141414424242424242424242424242424241212228288484848466666666121212121212141426666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1+i32−1−i32−1−i32
χ411111111111111111111111111111111111-111111111111111111111-1-1-1-1-1-1-111111111111111111111111111111111111-111111111111111111111-1-1-1-1-1-1-1
χ511111111111111111111111111111111111-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321−i321−i3211111111111111111111111111111111111-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-11+i321+i321−i321−i32
χ611111111111111111111111111111111111-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321+i321+i3211111111111111111111111111111111111-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-11−i321−i321+i321+i32
χ711111111111111111111111111111111-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11-111111111111111111111111111111111-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-111-11-11-1
χ811111111111111111111111111111111-1-1-11-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i3211-1−1−i321+i32−1+i321−i3211111111111111111111111111111111-1-1-11-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i3211-1−1−i321+i32−1+i321−i32
χ911111111111111111111111111111111-1-1-11-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i3211-1−1+i321−i32−1−i321+i3211111111111111111111111111111111-1-1-11-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i3211-1−1+i321−i32−1−i321+i32
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-1-111+i32−1−i321−i32−1+i3211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-1-111+i32−1−i321−i32−1+i32
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-1-111−i32−1+i321+i32−1−i3211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-1-111−i32−1+i321+i32−1−i32
χ1322-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1022-1-1-1-12222-1-1-1-122-1-1-1-1000000022-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1022-1-1-1-12222-1-1-1-122-1-1-1-10000000
χ1422-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1022-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32000000022-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1022-1-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i320000000
χ1522-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1022-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32000000022-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1022-1-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i320000000
χ1622-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2110-2-211112222-1-1-1-1-2-21111000000022-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2110-2-211112222-1-1-1-1-2-211110000000
χ1722-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2110-2-21111−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i32000000022-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2110-2-21111−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i320000000
χ1822-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2110-2-21111−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i32000000022-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2110-2-21111−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i320000000
χ192-22-222-2-222-2-2222-2-2-22222222-2-2-2-2-2-2-2000000000022-2-222-2-200000000000002-22-222-2-222-2-2222-2-2-22222222-2-2-2-2-2-2-2000000000022-2-222-2-20000000000000
χ202-22-222-2-222-2-2222-2-2-22222222-2-2-2-2-2-2-20000000000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300000000000002-22-222-2-222-2-2222-2-2-22222222-2-2-2-2-2-2-20000000000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i30000000000000
χ212-22-222-2-222-2-2222-2-2-22222222-2-2-2-2-2-2-20000000000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300000000000002-22-222-2-222-2-2222-2-2-22222222-2-2-2-2-2-2-20000000000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i30000000000000
χ222-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-1111111103−300033−3−322-2-2-1-111003−33−300000002-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-1111111103−300033−3−322-2-2-1-111003−33−30000000
χ232-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-1111111103−300033−3−3−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i3200ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ83−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ83−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ832ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ8300000002-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-1111111103−300033−3−3−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i3200ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ83−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ83−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ832ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ830000000
χ242-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-1111111103−300033−3−3−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i3200−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ832ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ83ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ83−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ8300000002-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-1111111103−300033−3−3−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i3200−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ832ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ83ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ83−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ830000000
χ252-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-111111110−33000−3−33322-2-2-1-11100−33−3300000002-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-111111110−33000−3−33322-2-2-1-11100−33−330000000
χ262-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-111111110−33000−3−333−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i3200−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ83ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ832ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ83−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ8300000002-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-111111110−33000−3−333−1−i3−1+i31+i31−i31+i321−i32−1−i32−1+i3200−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ83ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ832ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ83−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ830000000
χ272-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-111111110−33000−3−333−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i32002ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ83−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ83−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ83ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ8300000002-2-1122-2-2-1-111222-2-2-2-1-1-1-1-1-1-111111110−33000−3−333−1+i3−1−i31−i31+i31−i321+i32−1+i32−1−i32002ζ11+ζ19+2ζ23+ζ31+ζ43+2ζ47+ζ55+2ζ59+ζ67+2ζ71+ζ79+2ζ83−2ζ11−ζ19−2ζ23−ζ31−ζ43−2ζ47−ζ55−2ζ59−ζ67−2ζ71−ζ79−2ζ83−ζ11−2ζ19−ζ23−2ζ31−2ζ43−ζ47−2ζ55−ζ59−2ζ67−ζ71−2ζ79−ζ83ζ11+2ζ19+ζ23+2ζ31+2ζ43+ζ47+2ζ55+ζ59+2ζ67+ζ71+2ζ79+ζ830000000
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χ2966666-1-166666-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-600000000000000000000110000066666-1-166666-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-6000000000000000000001100000
χ306666-166-1-1-1-1-1-1-1-1-1-1-16-1-1-1-1-1-16-1-1-1-1-1-16660-1-1-1-1-1-10000000000000000000006666-166-1-1-1-1-1-1-1-1-1-1-16-1-1-1-1-1-16-1-1-1-1-1-16660-1-1-1-1-1-1000000000000000000000
χ316666-166-1-1-1-1-1-1-1-1-1-1-16-1-1-1-1-1-16-1-1-1-1-1-1-6-6-601111110000000000000000000006666-166-1-1-1-1-1-1-1-1-1-1-16-1-1-1-1-1-16-1-1-1-1-1-1-6-6-60111111000000000000000000000
χ3266-3-3-166-11+2121−2121+2121−212-1-1-1-1-1-1-31+2121+2121+2121−2121−2121−212-31+2121+2121+2121−2121−2121−2126-3-30-1-11+2121−2121+2121−21200000000000000000000066-3-3-166-11+2121−2121+2121−212-1-1-1-1-1-1-31+2121+2121+2121−2121−2121−212-31+2121+2121+2121−2121−2121−2126-3-30-1-11+2121−2121+2121−212000000000000000000000
χ3366-3-3-166-11+2121−2121+2121−212-1-1-1-1-1-1-31+2121+2121+2121−2121−2121−212-31+2121+2121+2121−2121−2121−212-633011−1−212−1+212−1−212−1+21200000000000000000000066-3-3-166-11+2121−2121+2121−212-1-1-1-1-1-1-31+2121+2121+2121−2121−2121−212-31+2121+2121+2121−2121−2121−212-633011−1−212−1+212−1−212−1+212000000000000000000000
χ3466-3-3-166-11−2121+2121−2121+212-1-1-1-1-1-1-31−2121−2121−2121+2121+2121+212-31−2121−2121−2121+2121+2121+2126-3-30-1-11−2121+2121−2121+21200000000000000000000066-3-3-166-11−2121+2121−2121+212-1-1-1-1-1-1-31−2121−2121−2121+2121+2121+212-31−2121−2121−2121+2121+2121+2126-3-30-1-11−2121+2121−2121+212000000000000000000000
χ3566-3-3-166-11−2121+2121−2121+212-1-1-1-1-1-1-31−2121−2121−2121+2121+2121+212-31−2121−2121−2121+2121+2121+212-633011−1+212−1−212−1+212−1−21200000000000000000000066-3-3-166-11−2121+2121−2121+212-1-1-1-1-1-1-31−2121−2121−2121+2121+2121+212-31−2121−2121−2121+2121+2121+212-633011−1+212−1−212−1+212−1−212000000000000000000000
χ366-66-66-11-666-6-6-1-1-1111-1-1-1-1-1-1-11111111000000000000000000000000−i7i7000006-66-66-11-666-6-6-1-1-1111-1-1-1-1-1-1-11111111000000000000000000000000−i7i700000
χ376-66-66-11-666-6-6-1-1-1111-1-1-1-1-1-1-11111111000000000000000000000000i7−i7000006-66-66-11-666-6-6-1-1-1111-1-1-1-1-1-1-11111111000000000000000000000000i7−i700000
χ386-66-6-16-61-1-111-1-1-11116-1-1-1-1-1-1-611111100007−77−7−770000000000000000000006-66-6-16-61-1-111-1-1-11116-1-1-1-1-1-1-611111100007−77−7−77000000000000000000000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.