Finite Group Databasebeta

← Group #13159707

Character table — Group #13159707

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
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χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
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χ1511-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-111-1-1-1-1-111111111-1-1-1-1ii−i−i−iii−ii−i−i−iii−iii−i
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χ1514-4-44-2-24-2-20022-2-442-22-222-422-222−22−22221-211-112-2-11-11-12-1-1000003i−3i003i−3i−3i3i00000−3i3i00−3i3i3i−3i−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ322−22−2−222−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−222222−2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000000000000000000000000000000
χ1524-4-44-2-24-2-20022-2-442-22-222-422-222−22−22221-211-112-2-11-11-12-1-100000−3i3i00−3i3i3i−3i000003i−3i003i−3i−3i3i−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ322−22−2−222−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−222222−2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000000000000000000000000000000
χ1534-4-44-2-24-2-20022-2-442-22-222-422-2−222222−221-211-112-2-11-11-12-1-1000003i−3i003i−3i−3i3i00000−3i3i00−3i3i3i−3i2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−222222−2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ322−22−2−222−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000000000000000000000000000000
χ1544-4-44-2-24-2-20022-2-442-22-222-422-2−222222−221-211-112-2-11-11-12-1-100000−3i3i00−3i3i3i−3i000003i−3i003i−3i−3i3i2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−222222−2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ322−22−2−222−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000000000000000000000000000000
χ1554-4-44-2-2-24-20022-22-2-442-2222-42-222−22−222211-21-11-112-2-11-1-12-1000003i−3i−3i3i003i−3i00000−3i3i3i−3i00−3i3i−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ322−22−2−222−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−222222−2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000000000000000000000000000000
χ1564-4-44-2-2-24-20022-22-2-442-2222-42-222−22−222211-21-11-112-2-11-1-12-100000−3i3i3i−3i00−3i3i000003i−3i−3i3i003i−3i−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ322−22−2−222−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−222222−2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000000000000000000000000000000
χ1574-4-44-2-2-24-20022-22-2-442-2222-42-2−222222−2211-21-11-112-2-11-1-12-1000003i−3i−3i3i003i−3i00000−3i3i3i−3i00−3i3i2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−222222−2−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ322−22−2−222−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000000000000000000000000000000
χ1584-4-44-2-2-24-20022-22-2-442-2222-42-2−222222−2211-21-11-112-2-11-1-12-100000−3i3i3i−3i00−3i3i000003i−3i−3i3i003i−3i2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−222222−2−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ322−22−2−222−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000000000000000000000000000000
χ1594-4-44-2-2-2-240022-22-22-2-442222-4-222−22−2222111-2-11-11-112-2-1-1-12000003i−3i3i−3i−3i3i0000000−3i3i−3i3i3i−3i00−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ322−22−2−2222−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−222222−2−200000000000000000000000000000000000000
χ1604-4-44-2-2-2-240022-22-22-2-442222-4-222−22−2222111-2-11-11-112-2-1-1-1200000−3i3i−3i3i3i−3i00000003i−3i3i−3i−3i3i00−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ322−22−2−2222−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−222222−2−200000000000000000000000000000000000000
χ1614-4-44-2-2-2-240022-22-22-2-442222-4-2−222222−22111-2-11-11-112-2-1-1-12000003i−3i3i−3i−3i3i0000000−3i3i−3i3i3i−3i002−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−222222−2−2−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ322−22−2−22200000000000000000000000000000000000000
χ1624-4-44-2-2-2-240022-22-22-2-442222-4-2−222222−22111-2-11-11-112-2-1-1-1200000−3i3i−3i3i3i−3i00000003i−3i3i−3i−3i3i002−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−222222−2−2−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ322−22−2−22200000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.