Finite Group Databasebeta

← Group #210201

Character table — Group #210201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444444444448888888888882224444444444488888888888888222444444488888888888888888844888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-11-1-111111111111-1-1-1-11111111111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-11-1-111111111111-1-1-1-111111111-1-11-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-111111111111111-1-1-111-1-1-111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1111111111111-1-11-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ171111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1-1iiii−i−i−i−i1i−iii−i−i1111-1-1-1-11111-1-1-11-1-1i−iii−i−iii−i−iii−i−i11-1-11-1i−ii−i1-1
χ181111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1-1iiii−i−i−i−i1i−iii−i−i1111-1-1-1-1-1-1-11-111-111i−i−i−iii−i−iiiii−i−i11-1-1-11−ii−ii-11
χ191111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1-1−i−i−i−iiiii1i−iii−i−i-1-1-1-111111111-1-1-11-1-1i−iii−i−iii−i−i−i−iii-1-111-11−ii−ii-11
χ201111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1-1−i−i−i−iiiii1i−iii−i−i-1-1-1-11111-1-1-11-111-111i−i−i−iii−i−iii−i−iii-1-1111-1i−ii−i1-1
χ211111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i-1-1-111iiii−i−i−i−i1i−i−i−iii1111-1-1-1-111-1-11-1-1-111−iiii−i−i−i−iii−i−iii-1-1111-1i−i−ii-11
χ221111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i-1-1-111iiii−i−i−i−i1i−i−i−iii1111-1-1-1-1-1-11-11111-1-1−ii−i−iiiii−i−i−i−iii-1-111-11−iii−i1-1
χ231111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i-1-1-111−i−i−i−iiiii1i−i−i−iii-1-1-1-1111111-1-11-1-1-111−iiii−i−i−i−iiiii−i−i11-1-1-11−iii−i1-1
χ241111-1-1-1-11111-1-1-1-1iiiiii−i−i−i−i−i−i-1-1-111−i−i−i−iiiii1i−i−i−iii-1-1-1-11111-1-11-11111-1-1−ii−i−iiiii−i−iii−i−i11-1-11-1i−i−ii-11
χ251111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii11-1-1-1iiii−i−i−i−i1−ii−i−iii-1-1-1-111111111-1-1-11-1-1−ii−i−iii−i−iiiii−i−i-1-111-11i−ii−i-11
χ261111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii11-1-1-1iiii−i−i−i−i1−ii−i−iii-1-1-1-11111-1-1-11-111-111−iiii−i−iii−i−iii−i−i-1-1111-1−ii−ii1-1
χ271111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii11-1-1-1−i−i−i−iiiii1−ii−i−iii1111-1-1-1-11111-1-1-11-1-1−ii−i−iii−i−iii−i−iii11-1-11-1−ii−ii1-1
χ281111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii11-1-1-1−i−i−i−iiiii1−ii−i−iii1111-1-1-1-1-1-1-11-111-111−iiii−i−iii−i−i−i−iii11-1-1-11i−ii−i-11
χ291111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii-1-1-111iiii−i−i−i−i1−iiii−i−i-1-1-1-1111111-1-11-1-1-111i−i−i−iiiii−i−i−i−iii11-1-1-11i−i−ii1-1
χ301111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii-1-1-111iiii−i−i−i−i1−iiii−i−i-1-1-1-11111-1-11-11111-1-1i−iii−i−i−i−iii−i−iii11-1-11-1−iii−i-11
χ311111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii-1-1-111−i−i−i−iiiii1−iiii−i−i1111-1-1-1-111-1-11-1-1-111i−i−i−iiiii−i−iii−i−i-1-1111-1−iii−i-11
χ321111-1-1-1-11111-1-1-1-1−i−i−i−i−i−iiiiiii-1-1-111−i−i−i−iiiii1−iiii−i−i1111-1-1-1-1-1-11-11111-1-1i−iii−i−i−i−iiiii−i−i-1-111-11i−i−ii1-1
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χ352222222222-2-222-2-2-2-2-2-222-2-2-2-22200-20000000000-2220000000000000020000-22-2000000-22-220000000000000000
χ362222222222-2-222-2-2-2-2-2-222-2-2-2-22200-20000000000-22200000000000000-200002-220000002-22-20000000000000000
χ3722222222-2-222-2-22222-2-22222-2-22222-22200000000-2-2-2222200000000000-2-200000-2-2000000000000000000000000
χ3822222222-2-222-2-22222-2-22222-2-222-2-2-2-2-200000000-2-2-2-2-2-2-200000000000220000022000000000000000000000000
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χ472222-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i0020000000000-22i−2i0000000000000020000-2-22000000−2i2i2i−2i0000000000000000
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χ502222-2-2-2-2-2-22222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-2-222200000000-2−2i2i−2i−2i2i2i000000000002-2000002i−2i000000000000000000000000
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χ522222-2-2-2-2-2-22222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-2-222200000000-22i−2i2i2i−2i−2i000000000002-200000−2i2i000000000000000000000000
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χ5822-2-22i2i−2i−2i002-2002i−2i2ζ−2ζ002ζ−2ζ2ζ3−2ζ3002ζ3−2ζ32-202i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0002ζ−2ζ2ζ3−2ζ3−2−222−i2−i2i2i200000000000000000000−1−i1+i−1+i1−i−22−i2i200000000
χ5922-2-22i2i−2i−2i002-2002i−2i2ζ−2ζ002ζ−2ζ2ζ3−2ζ3002ζ3−2ζ3-220−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000−2ζ2ζ−2ζ32ζ322−2−2i2i2−i2−i200000000000000000000−1−i1+i−1+i1−i−22−i2i200000000
χ6022-2-22i2i−2i−2i002-2002i−2i2ζ−2ζ002ζ−2ζ2ζ3−2ζ3002ζ3−2ζ3-220−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−2ζ2ζ−2ζ32ζ3−2−222−i2−i2i2i2000000000000000000001+i−1−i1−i−1+i2−2i2−i200000000
χ6122-2-22i2i−2i−2i002-2002i−2i−2ζ2ζ00−2ζ2ζ−2ζ32ζ300−2ζ32ζ32-202i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000−2ζ2ζ−2ζ32ζ3−2−222−i2−i2i2i2000000000000000000001+i−1−i1−i−1+i−22−i2i200000000
χ6222-2-22i2i−2i−2i002-2002i−2i−2ζ2ζ00−2ζ2ζ−2ζ32ζ300−2ζ32ζ32-202i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−2ζ2ζ−2ζ32ζ322−2−2i2i2−i2−i200000000000000000000−1−i1+i−1+i1−i2−2i2−i200000000
χ6322-2-22i2i−2i−2i002-2002i−2i−2ζ2ζ00−2ζ2ζ−2ζ32ζ300−2ζ32ζ3-220−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i0002ζ−2ζ2ζ3−2ζ3−2−222−i2−i2i2i200000000000000000000−1−i1+i−1+i1−i2−2i2−i200000000
χ6422-2-22i2i−2i−2i002-2002i−2i−2ζ2ζ00−2ζ2ζ−2ζ32ζ300−2ζ32ζ3-220−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i0002ζ−2ζ2ζ3−2ζ322−2−2i2i2−i2−i2000000000000000000001+i−1−i1−i−1+i−22−i2i200000000
χ6522-2-2−2i−2i2i2i002-200−2i2i2ζ3−2ζ3002ζ3−2ζ32ζ−2ζ002ζ−2ζ2-20−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0002ζ3−2ζ32ζ−2ζ−2−222i2i2−i2−i2000000000000000000001−i−1+i1+i−1−i−22i2−i200000000
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χ6722-2-2−2i−2i2i2i002-200−2i2i2ζ3−2ζ3002ζ3−2ζ32ζ−2ζ002ζ−2ζ-2202i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000−2ζ32ζ3−2ζ2ζ−2−222i2i2−i2−i200000000000000000000−1+i1−i−1−i1+i2−2−i2i200000000
χ6822-2-2−2i−2i2i2i002-200−2i2i2ζ3−2ζ3002ζ3−2ζ32ζ−2ζ002ζ−2ζ-2202i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−2ζ32ζ3−2ζ2ζ22−2−2−i2−i2i2i2000000000000000000001−i−1+i1+i−1−i−22i2−i200000000
χ6922-2-2−2i−2i2i2i002-200−2i2i−2ζ32ζ300−2ζ32ζ3−2ζ2ζ00−2ζ2ζ2-20−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000−2ζ32ζ3−2ζ2ζ22−2−2−i2−i2i2i2000000000000000000001−i−1+i1+i−1−i2−2−i2i200000000
χ7022-2-2−2i−2i2i2i002-200−2i2i−2ζ32ζ300−2ζ32ζ3−2ζ2ζ00−2ζ2ζ2-20−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−2ζ32ζ3−2ζ2ζ−2−222i2i2−i2−i200000000000000000000−1+i1−i−1−i1+i−22i2−i200000000
χ7122-2-2−2i−2i2i2i002-200−2i2i−2ζ32ζ300−2ζ32ζ3−2ζ2ζ00−2ζ2ζ-2202i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0002ζ3−2ζ32ζ−2ζ22−2−2−i2−i2i2i200000000000000000000−1+i1−i−1−i1+i−22i2−i200000000
χ7222-2-2−2i−2i2i2i002-200−2i2i−2ζ32ζ300−2ζ32ζ3−2ζ2ζ00−2ζ2ζ-2202i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0002ζ3−2ζ32ζ−2ζ−2−222i2i2−i2−i2000000000000000000001−i−1+i1+i−1−i2−2−i2i200000000
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χ884-4-444i−4i−4i4i-4400−4i4i0000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i4-400−4i4i00000000000000000000000000000000002i2−2i2−2i22i222−22−2222000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i4-400−4i4i0000000000000000000000000000000000−2i22i22i2−2i2−222222−22000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i-44004i−4i00000000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i-44004i−4i0000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000000000000

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