Finite Group Databasebeta

← Group #354534

Character table — Group #354534

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176
size11111111111111114444444444444444444444444444111111111111111144444444444444444444444444441111111111111111444444444444444444444444444411111111111111114444444444444444444444444444
order12222222444444442222444444448888888888888888444444444444444444444444444488888888888888882222222244444444222244444444888888888888888844444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ61111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ71111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
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χ1011111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i11111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
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χ1411111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii11111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i
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χ2122-22-2-22-22i−2i2i−2i2i−2i−2i2i002-20000002i−2i000000000000000022-22-2-22-22i−2i2i−2i2i−2i−2i2i002-20000002i−2i000000000000000022-22-2-22-22i−2i2i−2i2i−2i−2i2i002-20000002i−2i000000000000000022-22-2-22-22i−2i2i−2i2i−2i−2i2i002-20000002i−2i0000000000000000
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χ2822-2-22-2-22-2-2-222-222000000000000-222-200000000000022-2-22-2-22-2-2-222-222000000000000-222-200000000000022-2-22-2-22-2-2-222-222000000000000-222-200000000000022-2-22-2-22-2-2-222-222000000000000-222-2000000000000
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χ442-2-2-2-2222-2-22222-2-20000-222-2000000000000000000002-2-2-2-2222-2-22222-2-20000-222-2000000000000000000002-2-2-2-2222-2-22222-2-20000-222-2000000000000000000002-2-2-2-2222-2-22222-2-20000-222-200000000000000000000
χ4511111111111111111111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii-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−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ461111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii
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χ14211111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiiiii-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111ii−i−iii−i−iii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−i−i−i11-1-111-1-111-1-111-1-1
χ14311111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−iii−i−i11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1−i−iiiii−i−i−i−iiiii−i−iiiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii−i−iii-1-11111-1-1-1-11111-1-1
χ14411111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−iii−i−i-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1ii−i−i−i−iiiii−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii−i−iii11-1-1-1-11111-1-1-1-111
χ14511111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-1-1-1-111
χ14611111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i−i−iii-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1
χ14711111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−iii−i−i−i−i11-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1−i−iii−i−iiiii−i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iii−i−iiiii-1-111-1-11111-1-111-1-1
χ14811111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−iii−i−i−i−i-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1ii−i−iii−i−i−i−iii−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iii−i−iiiii11-1-111-1-1-1-111-1-111
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χ1762-2-2-2-2222-2-22222-2-20000-222-200000000000000000000−2i2i2i2i2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i00002i−2i−2i2i00000000000000000000-22222-2-2-222-2-2-2-22200002-2-22000000000000000000002i−2i−2i−2i−2i2i2i2i−2i−2i2i2i2i2i−2i−2i0000−2i2i2i−2i00000000000000000000

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