Finite Group Databasebeta

← Group #13147350

Character table — Group #13147350

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152
size1111111111112222229999999999991212121212121212121212121212121218181818181818181818181818181818181818181818181818181818181811111111111122222299999999999912121212121212121212121212121212181818181818181818181818181818181818181818181818181818181818
order123344661212121288242424242244666612121212336612121212242424242424242444448888881212121212121212242424242424242424242424226644661212121288242424242244666612121212666612121212242424242424242444448888881212121212121212242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111ii−i−i-1-1ii−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111ii−i−i-1-1ii−i−iiiii−i−i−i−i-1-1-1-1iiii−i−i−i−i
χ4111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−iii-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−iii-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii
χ5111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−i11−i−iiiiiii−i−i−i−i1111−i−i−i−iiiii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−i11−i−iiiiiii−i−i−i−i1111−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii11ii−i−i−i−i−i−iiiii1111iiii−i−i−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii11ii−i−i−i−i−i−iiiii1111iiii−i−i−i−i
χ91111-1-111-1-1-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−ii−i11-1-111-1-1ii−i−iii−i−iii−i−i1111-1-111-1-1-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-11-1i−ii−ii−i11-1-111-1-1ii−i−iii−i−iii−i−i
χ101111-1-111-1-1-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-11-11i−i−ii−ii-1-111-1-111ii−i−i−i−iii−i−iii1111-1-111-1-1-1-1i−iii−i−i11-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-11-11i−i−ii−ii-1-111-1-111ii−i−i−i−iii−i−iii
χ111111-1-111-1-1-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−ii−i−ii−ii-111-1ii−i−i−i−iii−i−iii-1-11111-1-11111-1-111-1-1-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−ii−i−ii−ii-111-1ii−i−i−i−iii−i−iii-1-11111-1-1
χ121111-1-111-1-1-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−iii−i−ii1-1-11−i−iiiii−i−i−i−iii11-1-1-1-1111111-1-111-1-1-1-1i−iii−i−i-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−iii−i−ii1-1-11−i−iiiii−i−i−i−iii11-1-1-1-111
χ131111-1-111-1-1-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii1111-1-111-1-1-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-11-1−ii−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii
χ141111-1-111-1-1-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-11-11−iii−ii−i-1-111-1-111−i−iiiii−i−iii−i−i1111-1-111-1-1-1-1−ii−i−iii11-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-11-11−iii−ii−i-1-111-1-111−i−iiiii−i−iii−i−i
χ151111-1-111-1-1-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiii−i−iii−i1-1-11ii−i−i−i−iiiii−i−i11-1-1-1-1111111-1-111-1-1-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiii−i−iii−i1-1-11ii−i−i−i−iiiii−i−i11-1-1-1-111
χ161111-1-111-1-1-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−iii−ii−i-111-1−i−iiiii−i−iii−i−i-1-11111-1-11111-1-111-1-1-1-1−ii−i−iii-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−iii−ii−i-111-1−i−iiiii−i−iii−i−i-1-11111-1-1
χ172-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000000000000000002-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i22-2-22i2i−2i−2i00000000000000000000000000000000000000
χ182-2222i−2i-2-22i2i−2i−2i000000-22−2i2i-2-222−2i−2i2i2i22-2-22i2i−2i−2i000000000000000000000000000000000000002-2222i−2i-2-22i2i−2i−2i000000-22−2i2i-2-222−2i−2i2i2i22-2-22i2i−2i−2i00000000000000000000000000000000000000
χ192-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000000000000000002-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00000000000000000000000000000000000000
χ202-222−2i2i-2-2−2i−2i2i2i000000-222i−2i-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000000000000000002-222−2i2i-2-2−2i−2i2i2i000000-222i−2i-2-2222i2i−2i−2i22-2-2−2i−2i2i2i00000000000000000000000000000000000000
χ2133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000ii−i−i11ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−1−i32−1+i32−1−i32−1+i32ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000ii−i−i11ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−1−i32−1+i32−1−i32−1+i32ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
χ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000−i−iii11−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22−1−i32−1+i32−1−i32−1+i32−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000−i−iii11−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22−1−i32−1+i32−1−i32−1+i32−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
χ2333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000001111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321+i321−i321+i321−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000001111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321+i321−i321+i321−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ2433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321+i321−i321+i321−i321−i321+i321−i321+i321−i321+i321−i321+i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321+i321−i321+i321−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ2533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000ii−i−i-1-1−i−iiiζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ221+i321−i321+i321−i32−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000ii−i−i-1-1−i−iiiζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ221+i321−i321+i321−i32−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
χ2633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000−i−iii-1-1ii−i−i−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ221+i321−i321+i321−i32ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000−i−iii-1-1ii−i−i−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ221+i321−i321+i321−i32ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
χ2733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i321−i321+i321−i321+i321−i321+i321−i321+i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ2833−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-11111111−i321+i321−i321+i321−i321+i321−i321+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i320000000000000000-1-1-1-11111111−i321+i321−i321+i321−i321+i321−i321+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
χ2933−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1411-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000i−i−iii−i-111-1ζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ22ζ14−ζ22−ζ141−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1411-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000i−i−iii−i-111-1ζ14ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ22ζ14−ζ22−ζ141−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32
χ3033−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1411-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000−iii−ii−i1-1-11−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22ζ22ζ14−ζ22−ζ14−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1411-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i320000000000000000−iii−ii−i1-1-11−ζ14−ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22ζ22ζ14−ζ22−ζ14−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32
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χ3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ14-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000-11-11−ii−ii−ii1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−ζ22−ζ14ζ22ζ14−ζ14−ζ22ζ14ζ22−ζ14−ζ22ζ14ζ2233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ14-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i320000000000000000-11-11−ii−ii−ii1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32−ζ22−ζ14ζ22ζ14−ζ14−ζ22ζ14ζ22−ζ14−ζ22ζ14ζ22
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.