Finite Group Databasebeta

← Group #13176674

Character table — Group #13176674

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size11222222222222244444444444444444444444444444444444444444444444121224242424242424242727363654545472721122222222222224444444444444444444444444444444444444444444444412122424242424242424272736365454547272
order1233333466666883333666612121212121212121212121212242424242424242424242424242424242424242424242424242444121212121212121244222886622666664666668866666666121212121212121212121212122424242424242424242424242424242424242424242424242424441212121212121212442228866
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111
χ51111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-11-1-11-11111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-11-1-11-1
χ61111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-11-111-111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-11-111-11
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χ81111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11-1-1111-11111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-11-1-1111-1
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χ1514-4-2-24-240-422-4222−22-2-24-222-420000000000000−22−2222−22−2222−22−2−222−2−2222222−22−22−2−2220000000000000000000-4422-42-404-2-24-2−222222-42-2-24-200000000000002−22−2−22222−2−222222−2−222−2−2−22−22222222−2−20000000000000000000
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χ1544-4-2-24-2-20222-4222−2211-21-1-12-100000−3i3i3i−3i00−3i3i−22−2222−22−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2−222−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000-4422-4220-2-2-24-2−2222-1-12-111-21000003i−3i−3i3i003i−3i2−22−2−22222−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ322−2−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000
χ1554-4-2-24-2-20222-42−222211-21-1-12-1000003i−3i−3i3i003i−3i2−22−2−22222−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ322−2−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000-4422-4220-2-2-24-222−22-1-12-111-2100000−3i3i3i−3i00−3i3i−22−2222−22−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−2−2222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000
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χ1614-4-2-2-24-202222-4−2222111-2-1-1-12000003i−3i3i−3i−3i3i002−22−22−2−22222−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ322−2−20000000000000000000-44222-420-2-2-2-2422−22-1-1-12111-200000−3i3i−3i3i3i−3i00−22−22−2222−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−2−2220000000000000000000
χ1624-4-2-2-24-202222-4−2222111-2-1-1-1200000−3i3i−3i3i3i−3i002−22−22−2−22222−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ322−2−20000000000000000000-44222-420-2-2-2-2422−22-1-1-12111-2000003i−3i3i−3i−3i3i00−22−22−2222−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−2−2220000000000000000000

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