Finite Group Databasebeta

← Group #207463

Character table — Group #207463

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size1111111111111111222222224444444444444444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444422444444444444444444444488888888888888888888888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-11-1-111-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111-111-1-11-1
χ9111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ10111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ11111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ12111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111-1-1-1111-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1111-1-1-11
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-11
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111-1
χ1711111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i111-11-1-1-1
χ1811111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii-1-1-11-1111
χ1911111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i-1-1-11-1111
χ2011111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii111-11-1-1-1
χ2111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ2211111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ2311111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ2411111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ2511111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii11-11-11-1-1
χ2611111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i-1-11-11-111
χ2711111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii-1-11-11-111
χ2811111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i11-11-11-1-1
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
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χ44222-2-2-2-2222-2-2-2-22222-2-222-2-200000000000000−2i2i−2i2i−2i2i−2i2i0000000000−2i−2i2i2i−2i−2i2i2i22-2-222-2-200000000000000000000000000000000
χ45222-2-2-2-2222-2-2-2-222-2-222-2-222000000000000002i−2i−2i2i2i−2i−2i2i002i2i−2i−2i2i2i−2i−2i000000000000000022-2-222-2-2000000000000000000000000
χ46222-2-2-2-2222-2-2-2-222-2-222-2-222000000000000002i−2i−2i2i2i−2i−2i2i00−2i−2i2i2i−2i−2i2i2i0000000000000000-2-222-2-222000000000000000000000000
χ47222-2-2-2-2222-2-2-2-222-2-222-2-22200000000000000−2i2i2i−2i−2i2i2i−2i002i2i−2i−2i2i2i−2i−2i0000000000000000-2-222-2-222000000000000000000000000
χ48222-2-2-2-2222-2-2-2-222-2-222-2-22200000000000000−2i2i2i−2i−2i2i2i−2i00−2i−2i2i2i−2i−2i2i2i000000000000000022-2-222-2-2000000000000000000000000
χ49222-2-2-2-22-2-22222-2-222-2-2-2-222000000000000002i−2i2i−2i−2i2i−2i2i000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ50222-2-2-2-22-2-22222-2-222-2-2-2-222000000000000002i−2i2i−2i−2i2i−2i2i0000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
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χ53222-2-2-2-22-2-22222-2-2-2-22222-2-2000000000000002i−2i−2i2i−2i2i2i−2i0022-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ54222-2-2-2-22-2-22222-2-2-2-22222-2-2000000000000002i−2i−2i2i−2i2i2i−2i00-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ55222-2-2-2-22-2-22222-2-2-2-22222-2-200000000000000−2i2i2i−2i2i−2i−2i2i0022-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
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χ5822-222-2-2-22i−2i2i2i−2i−2i2i−2i2-22-22i−2i2i−2i0000002-22-22i−2i2i−2i000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
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χ7022-222-2-2-2−2i2i−2i−2i2i2i−2i2i-22-222i−2i2i−2i0000002-2-22−2i2i2i−2i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ7122-222-2-2-2−2i2i−2i−2i2i2i−2i2i-22-222i−2i2i−2i000000-222-22i−2i−2i2i00000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000000000000000
χ7222-222-2-2-2−2i2i−2i−2i2i2i−2i2i-22-222i−2i2i−2i000000-222-22i−2i−2i2i0000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.