Finite Group Databasebeta

← Group #13158165

Character table — Group #13158165

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216C217C218C219C220C221C222C223C224C225C226C227C228C229C230C231C232C233C234C235C236C237C238C239C240C241C242C243C244C245C246C247C248C249C250C251C252
size111122222222224444444444441212121212121212121212121818181811112222222222444444444444121212121212121212121212181818181111222222222244444444444412121212121212121212121218181818111122222222224444444444441212121212121212121212121818181811112222222222444444444444121212121212121212121212181818181111222222222244444444444412121212121212121212121218181818
order1222334466666636661212121212121212444412121212121212128888366633121266666636661212121212121212121212121212121212121212242424243666331212666666366612121212121212121212121212121212121212122424242422226644666666666612121212121212124444121212121212121288886666661212666666666612121212121212121212121212121212121212122424242466666612126666666666121212121212121212121212121212121212121224242424
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χ21111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
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χ162222-12-2-2-12-12-12-1-1-1-11-21-211110000−i3i3−i3i3000000002222-12-2-2-12-12-12-1-1-1-11-21-211110000−i3i3−i3i3000000002222-12-2-2-12-12-12-1-1-1-11-21-211110000−i3i3−i3i3000000002222-12-2-2-12-12-12-1-1-1-11-21-211110000−i3i3−i3i3000000002222-12-2-2-12-12-12-1-1-1-11-21-211110000−i3i3−i3i3000000002222-12-2-2-12-12-12-1-1-1-11-21-211110000−i3i3−i3i300000000
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χ2181-11-111-11-1-111-1-11-1-1111-1-111-1-1−ii−ii−i−iii−i−iii11-1-1−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−ζ22ζ22−ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1−i32−1−i321+i321+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−ζ14ζ14−ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1+i32−1+i321−i321−i32-11-11-1-11-111-1-111-111-1-1-111-1-111i−ii−iii−i−iii−i−i-1-1111+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32ζ22−ζ22ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ221+i321+i32−1−i32−1−i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32ζ14−ζ14ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ141−i321−i32−1+i32−1+i32
χ219222222-2-22222222222-2-2-2-2-2-2-2-20000000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i31+i30000000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i31−i30000000000000000-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000001+i31+i31+i31+i31+i31+i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i31+i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i300000000000000001−i31−i31−i31−i31−i31−i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i31−i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i30000000000000000
χ22022222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100220000-1-1-1-10000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i3200−1−i3−1−i300001+i321+i321+i321+i320000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i3200−1+i3−1+i300001−i321−i321−i321−i320000-2-2-2-2-21-2-2-21-21-211111-21-21111100-2-20000111100001+i31+i31+i31+i31+i3−1−i321+i31+i31+i3−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32001+i31+i30000−1−i32−1−i32−1−i32−1−i3200001−i31−i31−i31−i31−i3−1+i321−i31−i31−i3−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32001−i31−i30000−1+i32−1+i32−1+i32−1+i320000
χ22122222-1222-12-12-1-1-1-1-12-12-1-1-1-1-100-2-2000011110000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32001+i31+i30000−1−i32−1−i32−1−i32−1−i320000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32001−i31−i30000−1+i32−1+i32−1+i32−1+i320000-2-2-2-2-21-2-2-21-21-211111-21-21111100220000-1-1-1-100001+i31+i31+i31+i31+i3−1−i321+i31+i31+i3−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i3200−1−i3−1−i300001+i321+i321+i321+i3200001−i31−i31−i31−i31−i3−1+i321−i31−i31−i3−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i3200−1+i3−1+i300001−i321−i321−i321−i320000
χ22222222-1-2-22-12-12-1-1-1-1-1-21-21111100000000−i3i3−i3i30000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i31+i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i3200000000−3+i323−i32−3+i323−i320000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i31−i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32000000003+i32−3−i323+i32−3−i320000-2-2-2-2-2122-21-21-2111112-12-1-1-1-1-100000000i3−i3i3−i300001+i31+i31+i31+i31+i3−1−i32−1−i3−1−i31+i3−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32000000003−i32−3+i323−i32−3+i3200001−i31−i31−i31−i31−i3−1+i32−1+i3−1+i31−i3−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i31−i32−1+i31−i321−i321−i321−i321−i3200000000−3−i323+i32−3−i323+i320000
χ22322222-1-2-22-12-12-1-1-1-1-1-21-21111100000000i3−i3i3−i30000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i31+i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32000000003−i32−3+i323−i32−3+i320000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i31−i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i3200000000−3−i323+i32−3−i323+i320000-2-2-2-2-2122-21-21-2111112-12-1-1-1-1-100000000−i3i3−i3i300001+i31+i31+i31+i31+i3−1−i32−1−i3−1−i31+i3−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i31+i32−1−i31+i321+i321+i321+i321+i3200000000−3+i323−i32−3+i323−i3200001−i31−i31−i31−i31−i3−1+i32−1+i3−1+i31−i3−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32000000003+i32−3−i323+i32−3−i320000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.