Finite Group Databasebeta

← Group #207706

Character table — Group #207706

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444444444444444444444444224444444444888888888888888888888888888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-1-1-111iiii−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-11111-1-1−i−i−i−iiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-1-1-111−i−i−i−iiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-11111-1-1iiii−i−i−i−i
χ91111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11-1-111-1-111
χ111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-111-1-111
χ121111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-11-1-111-1111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1-1-1-1111-1ii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1111-1-1-11−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1-1-1-1111-1−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1111-1-1-11ii−i−i−i−iii
χ17111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i111-11-1-1-1i−ii−ii−ii−i
χ18111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-11-1111−ii−ii−ii−ii
χ19111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii111-11-1-1-1−ii−ii−ii−ii
χ20111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-1-11-1111i−ii−ii−ii−i
χ21111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-11-1-11-11-1-11-11
χ22111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-11-111-11-111-11-1
χ23111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-11-11-1-1-11-111-11-1
χ24111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11-11-1111-11-1-11-11
χ25111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1-11-11i−i−iii−i−ii
χ26111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-11-111-11-1−iii−i−iii−i
χ27111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1-11-11−iii−i−iii−i
χ28111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-111-11-1i−i−iii−i−ii
χ29111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-111-1-111-1-11-111-1
χ30111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-111-1-111-11-1-11
χ31111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-11-111-11-1-11
χ32111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-111-11-1-11-111-1
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χ3522222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-22222000000000000000000000000000000000000000000000000
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χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2222222-2-2000000000000000000000000000000000000000000000000
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χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-222-2-222000000000000000000000000000000000000000000000000
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χ7822-2-2-222-22-2-220000-2-2220000000000002i2i−2i−2i−2i2i2i−2i−2i2i2i−2i00-220000002i−2i−2ζ32ζ32ζ3−2ζ300002ζ3−2ζ3−2ζ32ζ300000000−2ζ2ζ2ζ−2ζ0000−2ζ2ζ2ζ−2ζ0000000000000000
χ7922-2-2-222-22-2-220000-2-222000000000000−2i−2i2i2i2i−2i−2i2i2i−2i−2i2i00-22000000−2i2i2ζ−2ζ−2ζ2ζ0000−2ζ2ζ2ζ−2ζ000000002ζ3−2ζ3−2ζ32ζ300002ζ3−2ζ3−2ζ32ζ30000000000000000
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χ8622-2-2-222-2-222-20000-2-2220000000000002i2i−2i−2i−2i2i2i−2i2i−2i−2i2i002-2000000−2i2i0000−2ζ32ζ32ζ3−2ζ300002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000−2ζ2ζ2ζ−2ζ00000000000000000000
χ8722-2-2-222-2-222-20000-2-222000000000000−2i−2i2i2i2i−2i−2i2i−2i2i2i−2i002-20000002i−2i00002ζ−2ζ−2ζ2ζ0000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300002ζ3−2ζ3−2ζ32ζ300000000000000000000
χ8822-2-2-222-2-222-20000-2-222000000000000−2i−2i2i2i2i−2i−2i2i−2i2i2i−2i002-20000002i−2i0000−2ζ2ζ2ζ−2ζ00002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000−2ζ32ζ32ζ3−2ζ300000000000000000000
χ894-444-44-4-40000000000004i−4i4i−4i4-44-400004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ904-444-44-4-40000000000004i−4i4i−4i-44-440000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ914-444-44-4-4000000000000−4i4i−4i4i4-44-40000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ924-444-44-4-4000000000000−4i4i−4i4i-44-4400004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ934-44-44-44-4000000004-44-400004i−4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ944-44-44-44-4000000004-44-40000−4i4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ954-44-44-44-400000000-44-4400004i−4i−4i4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ964-44-44-44-400000000-44-440000−4i4i4i−4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4-44-4-44400004-44-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ984-4-44-4-44400004-44-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-44-4-4440000-44-444-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-4-44-4-4440000-44-44-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-444-4400004-4-440000000000004-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4-444-4400004-4-44000000000000-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-444-440000-444-40000000000004-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-440000-444-4000000000000-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000

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