Finite Group Databasebeta

← Group #207702

Character table — Group #207702

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444444444444444444444444444444444444444888888888888888888888888888888884444444488888888
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−i1111-1-1-1-1iiii−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-1-1-1-11111−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−iiiiiiiiiiiiiiiii1111-1-1-1-1−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-1-1-1-11111iiii−i−i−i−i
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−iii−i−iii
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111ii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ17111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ18111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ19111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ20111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ21111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-111-11-1-11-11
χ22111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-11-1-11-111-11-1
χ23111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-1-11-11-11-111-11-1
χ24111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-111-11-11-11-1-11-11
χ25111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-11
χ26111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-111-1
χ27111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-11-111-1-111-1
χ28111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-11-1-111-1-11
χ29111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1i−i−ii−iii−i
χ30111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11−iii−ii−i−ii
χ31111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1−iii−ii−i−ii
χ32111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-11-1-11i−i−ii−iii−i
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χ3622222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222222222-2-2000000000000000000000000000000000000000000000000
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χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-22222-2-222000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
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χ742-2-222-2-222-2-222i2i−2i−2i000000000000000022-2-22i−2i−2i2i2i−2i−2i2i2i−2i000000002-2−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
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χ792-2-222-2-222-2-22−2i−2i2i2i0000000000000000-2-2222i−2i−2i2i2i−2i−2i2i−2i2i00000000-222ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000
χ802-2-222-2-222-2-22−2i−2i2i2i0000000000000000-2-2222i−2i−2i2i2i−2i−2i2i−2i2i00000000-22−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000
χ812-2-222-2-22-222-22i2i−2i−2i000000000000000022-2-22i−2i−2i2i−2i2i2i−2i−2i2i00000000-22000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
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χ832-2-222-2-22-222-22i2i−2i−2i0000000000000000-2-222−2i2i2i−2i2i−2i−2i2i−2i2i000000002-2000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ842-2-222-2-22-222-22i2i−2i−2i0000000000000000-2-222−2i2i2i−2i2i−2i−2i2i−2i2i000000002-200000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ852-2-222-2-22-222-2−2i−2i2i2i000000000000000022-2-2−2i2i2i−2i2i−2i−2i2i2i−2i00000000-22000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ862-2-222-2-22-222-2−2i−2i2i2i000000000000000022-2-2−2i2i2i−2i2i−2i−2i2i2i−2i00000000-2200000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ872-2-222-2-22-222-2−2i−2i2i2i0000000000000000-2-2222i−2i−2i2i−2i2i2i−2i2i−2i000000002-2000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ882-2-222-2-22-222-2−2i−2i2i2i0000000000000000-2-2222i−2i−2i2i−2i2i2i−2i2i−2i000000002-200000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ894444-4-4-4-400004-44-44-44-44-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ904444-4-4-4-400004-44-4-44-44-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ914444-4-4-4-40000-44-444-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ924444-4-4-4-40000-44-44-44-444-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9344-4-4-4-4440000000000004i−4i−4i4i00004i−4i4i−4i4-44-400000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-4-4-4440000000000004i−4i−4i4i0000−4i4i−4i4i-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-4-4-444000000000000−4i4i4i−4i00004i−4i4i−4i-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-4-444000000000000−4i4i4i−4i0000−4i4i−4i4i4-44-400000000000000000000000000000000000000000000000000000000000000000000
χ974-44-4-44-44000000004i−4i−4i4i00004i−4i4i−4i00004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ984-44-4-44-44000000004i−4i−4i4i0000−4i4i−4i4i0000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ994-44-4-44-4400000000−4i4i4i−4i00004i−4i4i−4i0000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-44-4400000000−4i4i4i−4i0000−4i4i−4i4i00004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ1014-4-44-444-400004i−4i−4i4i000000004i−4i−4i4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-44-444-400004i−4i−4i4i00000000−4i4i4i−4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-444-40000−4i4i4i−4i000000004i−4i−4i4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-40000−4i4i4i−4i00000000−4i4i4i−4i4-4-44000000000000000000000000000000000000000000000000000000000000000000000000

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