Finite Group Databasebeta

← Group #72259851

Character table — Group #72259851

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216C217C218C219C220C221C222C223C224C225C226C227C228C229C230C231C232C233C234C235C236C237C238C239C240
size11222222222224444444444444444444444444444441212121224242424242424242424363672112222222222244444444444444444444444444444412121212242424242424242424243636721122222222222444444444444444444444444444444121212122424242424242424242436367211222222222224444444444444444444444444444441212121224242424242424242424363672
order12233446612121212344666661212121212121212121212121212121212121212121222446688121224242424222444121244121212121212124412121212121212121212121212121212121212121212121212121244441212881212242424244442226644661212121264466666121212121212121212121212121212121212121212122244668812122424242422244412124412121212121212441212121212121212121212121212121212121212121212121212124444121288121224242424444
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χ31111111111111111111111111111111111111111111-11-11-11-11-11-1-111-1-1-11111111111111111111111111111111111111111111-11-11-11-11-11-1-111-1-1-11111111111111111111111111111111111111111111-11-11-11-11-11-1-111-1-1-11111111111111111111111111111111111111111111-11-11-11-11-11-1-111-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
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χ2294-40-24002-423−2300-22-2002000023−2300−1+31−3−1−31+32-22-2−1+31−3−1−31+3−1+31−3−1−31+300000000000000000−4i4i02i−4i00−2i4i−2i32i3002i−2i2i00−2i0000−2i32i300−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2i−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000-4402-400-24−2323002-2200-20000−2323001−3−1+31+3−1−3-22-221−3−1+31+3−1−31−3−1+31+3−1−3000000000000000004i−4i0−2i4i002i−4i2i3−2i300−2i2i−2i002i00002i3−2i300ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2i2i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000
χ2304-40-24002-423−2300-2-22002000023−23001−3−1+31+3−1−3-22-221−3−1+31+3−1−31−3−1+31+3−1−300000000000000000−4i4i02i−4i00−2i4i−2i32i3002i2i−2i00−2i0000−2i32i300ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ112i−2i2i−2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000-4402-400-24−23230022-200-20000−232300−1+31−3−1−31+32-22-2−1+31−3−1−31+3−1+31−3−1−31+3000000000000000004i−4i0−2i4i002i−4i2i3−2i300−2i−2i2i002i00002i3−2i300−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−2i2i−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000
χ2314-40-24002-4−232300-22-20020000−232300−1−31+3−1+31−32-22-2−1−31+3−1+31−3−1−31+3−1+31−300000000000000000−4i4i02i−4i00−2i4i2i3−2i3002i−2i2i00−2i00002i3−2i300ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2i−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000-4402-400-2423−23002-2200-2000023−23001+3−1−31−3−1+3-22-221+3−1−31−3−1+31+3−1−31−3−1+3000000000000000004i−4i0−2i4i002i−4i−2i32i300−2i2i−2i002i0000−2i32i300−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2i2i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000
χ2324-40-24002-4−232300-2-220020000−2323001+3−1−31−3−1+3-22-221+3−1−31−3−1+31+3−1−31−3−1+300000000000000000−4i4i02i−4i00−2i4i2i3−2i3002i2i−2i00−2i00002i3−2i300−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ112i−2i2i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000-4402-400-2423−230022-200-2000023−2300−1−31+3−1+31−32-22-2−1−31+3−1+31−3−1−31+3−1+31−3000000000000000004i−4i0−2i4i002i−4i−2i32i300−2i−2i2i002i0000−2i32i300ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−2i2i−2i2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000
χ2334-40-2-2002223−2323−2312-200-13-300−33−33−1+31−3−1−31+3−1+31−3−1−31+32−3−2+3-11-112+3−2−300000000000000000−4i4i02i2i00−2i−2i−2i32i3−2i32i3−i−2i2i00i−3i3i00i3−i3i3−i3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11i−ii−i−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ1100000000000000000-4402200-2-2−2323−2323-1-22001-33003−33−31−3−1+31+3−1−31−3−1+31+3−1−3−2+32−31-11-1−2−32+3000000000000000004i−4i0−2i−2i002i2i2i3−2i32i3−2i3i2i−2i00−i3i−3i00−i3i3−i3i3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ii−iiζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ1100000000000000000
χ2344-40-2-2002223−2323−231-2200-13-300−33−331−3−1+31+3−1−31−3−1+31+3−1−3−2+32−31-11-1−2−32+300000000000000000−4i4i02i2i00−2i−2i−2i32i3−2i32i3−i2i−2i00i−3i3i00i3−i3i3−i3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ii−iiζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ1100000000000000000-4402200-2-2−2323−2323-12-2001-33003−33−3−1+31−3−1−31+3−1+31−3−1−31+32−3−2+3-11-112+3−2−3000000000000000004i−4i0−2i−2i002i2i2i3−2i32i3−2i3i−2i2i00−i3i−3i00−i3i3−i3i3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11i−ii−i−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ1100000000000000000
χ2354-40-2-2002223−23−232312-200-1-3300−333−3−1+31−3−1−31+3−1−31+3−1+31−3-112+3−2−32−3−2+3-1100000000000000000−4i4i02i2i00−2i−2i−2i32i32i3−2i3−i−2i2i00i3i−3i00i3−i3−i3i3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11i−i−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11i−i00000000000000000-4402200-2-2−232323−23-1-220013-3003−3−331−3−1+31+3−1−31+3−1−31−3−1+31-1−2−32+3−2+32−31-1000000000000000004i−4i0−2i−2i002i2i2i3−2i3−2i32i3i2i−2i00−i−3i3i00−i3i3i3−i3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−iiζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ii00000000000000000
χ2364-40-2-2002223−23−23231-2200-1-3300−333−31−3−1+31+3−1−31+3−1−31−3−1+31-1−2−32+3−2+32−31-100000000000000000−4i4i02i2i00−2i−2i−2i32i32i3−2i3−i2i−2i00i3i−3i00i3−i3−i3i3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−iiζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ii00000000000000000-4402200-2-2−232323−23-12-20013-3003−3−33−1+31−3−1−31+3−1−31+3−1+31−3-112+3−2−32−3−2+3-11000000000000000004i−4i0−2i−2i002i2i2i3−2i3−2i32i3i−2i2i00−i−3i3i00−i3i3i3−i3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11i−i−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11i−i00000000000000000
χ2374-40-2-20022−232323−2312-200-1-33003−3−33−1−31+3−1+31−3−1+31−3−1−31+3-112−3−2+32+3−2−3-1100000000000000000−4i4i02i2i00−2i−2i2i3−2i3−2i32i3−i−2i2i00i3i−3i00−i3i3i3−i3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11i−iζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11i−i00000000000000000-4402200-2-223−23−2323-1-220013-300−333−31+3−1−31−3−1+31−3−1+31+3−1−31-1−2+32−3−2−32+31-1000000000000000004i−4i0−2i−2i002i2i−2i32i32i3−2i3i2i−2i00−i−3i3i00i3−i3−i3i3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ii−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ii00000000000000000
χ2384-40-2-20022−232323−231-2200-1-33003−3−331+3−1−31−3−1+31−3−1+31+3−1−31-1−2+32−3−2−32+31-100000000000000000−4i4i02i2i00−2i−2i2i3−2i3−2i32i3−i2i−2i00i3i−3i00−i3i3i3−i3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ii−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ii00000000000000000-4402200-2-223−23−2323-12-20013-300−333−3−1−31+3−1+31−3−1+31−3−1−31+3-112−3−2+32+3−2−3-11000000000000000004i−4i0−2i−2i002i2i−2i32i32i3−2i3i−2i2i00−i−3i3i00i3−i3−i3i3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11i−iζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11i−i00000000000000000
χ2394-40-2-20022−2323−232312-200-13-3003−33−3−1−31+3−1+31−3−1−31+3−1+31−32+3−2−3-11-112−3−2+300000000000000000−4i4i02i2i00−2i−2i2i3−2i32i3−2i3−i−2i2i00i−3i3i00−i3i3−i3i3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11i−ii−iζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ1100000000000000000-4402200-2-223−2323−23-1-22001-3300−33−331+3−1−31−3−1+31+3−1−31−3−1+3−2−32+31-11-1−2+32−3000000000000000004i−4i0−2i−2i002i2i−2i32i3−2i32i3i2i−2i00−i3i−3i00i3−i3i3−i3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ii−ii−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ1100000000000000000
χ2404-40-2-20022−2323−23231-2200-13-3003−33−31+3−1−31−3−1+31+3−1−31−3−1+3−2−32+31-11-1−2+32−300000000000000000−4i4i02i2i00−2i−2i2i3−2i32i3−2i3−i2i−2i00i−3i3i00−i3i3−i3i3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ii−ii−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ1100000000000000000-4402200-2-223−2323−23-12-2001-3300−33−33−1−31+3−1+31−3−1−31+3−1+31−32+3−2−3-11-112−3−2+3000000000000000004i−4i0−2i−2i002i2i−2i32i3−2i32i3i−2i2i00−i3i−3i00i3−i3i3−i3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11i−ii−iζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ1100000000000000000

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