Finite Group Databasebeta

← Group #13174428

Character table — Group #13174428

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216C217C218C219C220C221C222C223C224C225C226C227C228C229C230C231C232C233C234
size112222222222244444444444412121212121212121212121236361122222222222444444444444121212121212121212121212363611222222222224444444444441212121212121212121212123636112222222222244444444444412121212121212121212121236361122222222222444444444444121212121212121212121212363611222222222224444444444441212121212121212121212123636
order12233446666121236666121212121212122266668824242424243663312126666121236666121212121212126666662424242424246123663312126666121236666121212121212126666662424242424246122226644666612126666612121212121212226666882424242424666661212666612126666612121212121212666666242424242424612666661212666612126666612121212121212666666242424242424612
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1111111-1-11111111111111111111111111-1-1-1-1-1-1111111-1-11111111111111111111111111-1-1-1-1-1-1111111-1-11111111111111111111111111-1-1-1-1-1-1111111-1-11111111111111111111111111-1-1-1-1-1-1111111-1-11111111111111111111111111-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ511-111-11-1-111111-1-1-111-1-111-1-11-111-1-11-111-1-11-111-111-11-1-111111-1-1-111-1-111-1-11-111-1-11-111-1-11-111-111-11-1-111111-1-1-111-1-111-1-11-111-1-11-111-1-11-111-111-11-1-111111-1-1-111-1-111-1-11-111-1-11-111-1-11-111-111-11-1-111111-1-1-111-1-111-1-11-111-1-11-111-1-11-111-111-11-1-111111-1-1-111-1-111-1-11-111-1-11-111-1-11-1
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χ711-111-11-1-111111-1-1-111-1-111-1-1-11-1-1111-111-1-1-1111-111-11-1-111111-1-1-111-1-111-1-1-11-1-1111-111-1-1-1111-111-11-1-111111-1-1-111-1-111-1-1-11-1-1111-111-1-1-1111-111-11-1-111111-1-1-111-1-111-1-1-11-1-1111-111-1-1-1111-111-11-1-111111-1-1-111-1-111-1-1-11-1-1111-111-1-1-1111-111-11-1-111111-1-1-111-1-111-1-1-11-1-1111-111-1-1-11
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χ112222-122-1-12-122-12-1-1-1-12-1-1-1-1-1-2-21111000000002222-122-1-12-122-12-1-1-1-12-1-1-1-1-1-2-21111000000002222-122-1-12-122-12-1-1-1-12-1-1-1-1-1-2-21111000000002222-122-1-12-122-12-1-1-1-12-1-1-1-1-1-2-21111000000002222-122-1-12-122-12-1-1-1-12-1-1-1-1-1-2-21111000000002222-122-1-12-122-12-1-1-1-12-1-1-1-1-1-2-2111100000000
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χ16211-111-11-1-111111-1-1-111-1-111-1-11-111-1-1-11-1-111-11−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32-1-11-1-11-111-1-1-1-1-1111-1-111-1-111-11-1-1111-111-1-11-11−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
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χ16411-111-11-1-111111-1-1-111-1-111-1-1-11-1-111-11-1-1111-1−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32-1-11-1-11-111-1-1-1-1-1111-1-111-1-1111-111-1-11-111-1-1-111−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32
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χ170222-122222-12-1-1-1-1-1-1-12-12-1-1-1-100000022-1-1-1-100−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i321−i321−i32000000−1+i3−1+i31−i321−i321−i321−i3200−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i321+i321+i32000000−1−i3−1−i31+i321+i321+i321+i3200-2-2-21-2-2-2-2-21-21111111-21-21111000000-2-21111001−i31−i31−i3−1+i321−i31−i31−i31−i31−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i320000001−i31−i3−1+i32−1+i32−1+i32−1+i32001+i31+i31+i3−1−i321+i31+i31+i31+i31+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i320000001+i31+i3−1−i32−1−i32−1−i32−1−i3200
χ171222-122222-12-1-1-1-1-1-1-12-12-1-1-1-1000000-2-2111100−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i31−i32−1+i31−i321−i321−i321−i320000001−i31−i3−1+i32−1+i32−1+i32−1+i3200−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i31+i32−1−i31+i321+i321+i321+i320000001+i31+i3−1−i32−1−i32−1−i32−1−i3200-2-2-21-2-2-2-2-21-21111111-21-2111100000022-1-1-1-1001−i31−i31−i3−1+i321−i31−i31−i31−i31−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i3−1+i321−i3−1+i32−1+i32−1+i32−1+i32000000−1+i3−1+i31−i321−i321−i321−i32001+i31+i31+i3−1−i321+i31+i31+i31+i31+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i3−1−i321+i3−1−i32−1−i32−1−i32−1−i32000000−1−i3−1−i31+i321+i321+i321+i3200
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χ1991111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111−1−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−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+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+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+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−i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−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+i321−i321−i32
χ20011-111-11-1-111111-1-1-111-1-111-1-11-111-1-11-111-1-11-1−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i32-1-11-1-11-111-1-1-1-1-1111-1-111-1-111-11-1-111-11-1-111-111+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32
χ20111-111-11-1-111111-1-1-111-1-111-1-11-111-1-1-11-1-111-11−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32-1-11-1-11-111-1-1-1-1-1111-1-111-1-111-11-1-1111-111-1-11-11+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ20211-111-11-1-111111-1-1-111-1-111-1-1-11-1-1111-111-1-1-11−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32-1-11-1-11-111-1-1-1-1-1111-1-111-1-1111-111-1-1-11-1-1111-11+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ20311-111-11-1-111111-1-1-111-1-111-1-1-11-1-111-11-1-1111-1−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32-1-11-1-11-111-1-1-1-1-1111-1-111-1-1111-111-1-11-111-1-1-111+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32
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χ2324-40-2-200−2i32i322−232310i3−i3-10003−3−3i3i00000000000000−2−2i32+2i301+i31+i300−3+i33−i3−1−i3−1−i3−4ζ7−2ζ114ζ7+2ζ11−1−i3203−i32−3+i321+i320002ζ7+ζ11−2ζ7−ζ11−3ζ113ζ1100000000000000−2+2i32−2i301−i31−i3003+i3−3−i3−1+i3−1+i32ζ7+4ζ11−2ζ7−4ζ11−1+i320−3−i323+i321−i32000−ζ7−2ζ11ζ7+2ζ11−3ζ73ζ700000000000000-44022002i3−2i3-2-223−23-10−i3i31000−333i−3i000000000000002+2i3−2−2i30−1−i3−1−i3003−i3−3+i31+i31+i34ζ7+2ζ11−4ζ7−2ζ111+i320−3+i323−i32−1−i32000−2ζ7−ζ112ζ7+ζ113ζ11−3ζ11000000000000002−2i3−2+2i30−1+i3−1+i300−3−i33+i31−i31−i3−2ζ7−4ζ112ζ7+4ζ111−i3203+i32−3−i32−1+i32000ζ7+2ζ11−ζ7−2ζ113ζ7−3ζ700000000000000
χ2334-40-2-2002i3−2i32223−2310−i3i3-1000−33−3i3i00000000000000−2−2i32+2i301+i31+i3003−i3−3+i3−1−i3−1−i34ζ7+2ζ11−4ζ7−2ζ11−1−i320−3+i323−i321+i32000−2ζ7−ζ112ζ7+ζ11−3ζ113ζ1100000000000000−2+2i32−2i301−i31−i300−3−i33+i3−1+i3−1+i3−2ζ7−4ζ112ζ7+4ζ11−1+i3203+i32−3−i321−i32000ζ7+2ζ11−ζ7−2ζ11−3ζ73ζ700000000000000-4402200−2i32i3-2-2−2323-10i3−i310003−33i−3i000000000000002+2i3−2−2i30−1−i3−1−i300−3+i33−i31+i31+i3−4ζ7−2ζ114ζ7+2ζ111+i3203−i32−3+i32−1−i320002ζ7+ζ11−2ζ7−ζ113ζ11−3ζ11000000000000002−2i3−2+2i30−1+i3−1+i3003+i3−3−i31−i31−i32ζ7+4ζ11−2ζ7−4ζ111−i320−3−i323+i32−1+i32000−ζ7−2ζ11ζ7+2ζ113ζ7−3ζ700000000000000
χ2344-40-2-2002i3−2i322−232310−i3i3-10003−33i−3i00000000000000−2−2i32+2i301+i31+i3003−i3−3+i3−1−i3−1−i3−4ζ7−2ζ114ζ7+2ζ11−1−i320−3+i323−i321+i320002ζ7+ζ11−2ζ7−ζ113ζ11−3ζ1100000000000000−2+2i32−2i301−i31−i300−3−i33+i3−1+i3−1+i32ζ7+4ζ11−2ζ7−4ζ11−1+i3203+i32−3−i321−i32000−ζ7−2ζ11ζ7+2ζ113ζ7−3ζ700000000000000-4402200−2i32i3-2-223−23-10i3−i31000−33−3i3i000000000000002+2i3−2−2i30−1−i3−1−i300−3+i33−i31+i31+i34ζ7+2ζ11−4ζ7−2ζ111+i3203−i32−3+i32−1−i32000−2ζ7−ζ112ζ7+ζ11−3ζ113ζ11000000000000002−2i3−2+2i30−1+i3−1+i3003+i3−3−i31−i31−i3−2ζ7−4ζ112ζ7+4ζ111−i320−3−i323+i32−1+i32000ζ7+2ζ11−ζ7−2ζ11−3ζ73ζ700000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.