Finite Group Databasebeta

← Group #219829

Character table — Group #219829

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222444444444444444444444444444444444444888888888888888888888888224444444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
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χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-111ii−i−iii−i−iii−i−i−i−iii−i−iii-11-11
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-111−i−iii−i−iii−i−iiiii−i−iii−i−i-11-11
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii1-11-1
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-111-1-1ii−i−i−i−iii−i−iii−i−iii−i−iii-11-11
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii−i−iii1-11-1
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-111-1-1−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-11
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-11111-1-1−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-1
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11-1-11111-1-1ii−i−i−i−iiiii−i−iii−i−i−i−iii-111-1
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11
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χ3111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-11
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-111-1-1-1-111ii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1
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χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000-22-2200000000000000000000000000000000
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χ3722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-22222-2-222-2-2000000000000000000000000-2-22200000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-222-2-222-2-22200000000000000000000000022-2-200000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-222-2-2-2-222000000000000000000000000-222-200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-22222-2-20000000000000000000000002-2-2200000000000000000000000000000000
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χ662-22-22-22-22i−2i−2i2i−2i2i−2i2i2-22-22i−2i2i−2i2-22-22i−2i−2i2i2-22i−2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000000000000000
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χ742-22-22-22-2−2i2i2i−2i2i−2i2i−2i2-22-2−2i2i−2i2i2-22-2−2i2i2i−2i2-2−2i2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000000000000000
χ752-22-22-22-2−2i2i2i−2i2i−2i2i−2i2-22-2−2i2i−2i2i-22-222i−2i−2i2i-222i−2i0000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000
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χ782-22-22-22-2−2i2i2i−2i2i−2i2i−2i-22-222i−2i2i−2i2-22-2−2i2i2i−2i-222i−2i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000000000000000
χ792-22-22-22-2−2i2i2i−2i2i−2i2i−2i-22-222i−2i2i−2i-22-222i−2i−2i2i2-2−2i2i0000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ802-22-22-22-2−2i2i2i−2i2i−2i2i−2i-22-222i−2i2i−2i-22-222i−2i−2i2i2-2−2i2i000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000
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χ9744-4-44-4-44−4i4i4i4i−4i−4i−4i4i000000000000000000000000000000000000000000002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000
χ9844-4-44-4-44−4i4i4i4i−4i−4i−4i4i00000000000000000000000000000000000000000000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000
χ994-4-4444-4-4444-4-44-4-400000000000000000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ1004-4-4444-4-4444-4-44-4-4000000000000000000000000000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ1014-4-4444-4-4-4-4-444-4440000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ1024-4-4444-4-4-4-4-444-444000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ1034-4-4-4-444444-444-4-4-400000000-444-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4444-4-44-4-444400000000-444-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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