Finite Group Databasebeta

← Group #141320

Character table — Group #141320

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122244444444444488888888888888882488888888888888888888888888888888161616161616161616161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ101111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ121111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11
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χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
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χ20222222222222-2-2-2-22222000000002222-2-2-2-2-2-2000000000000-2-222-2-2220000000000000000000000000000
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χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-2-2-222220000222222220000-2-20000-2-2-2-200000000000000000000000022−2−222−2−222−2−222−2−20000
χ2422222222-2-2-2-222220000222222220000-2-20000-2-2-2-2000000000000000000000000−2−222−2−222−2−222−2−2220000
χ2522222222-2-2-2-222220000-2-2-2-2-2-2-2-20000-2-20000222200000000000000000000000022−2−222−2−2−2−222−2−2220000
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χ322222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222222222-22-2-222-2-2222222-2-2-2-2000000000000000000000000000000000000
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χ392-22-22i2i−2i−2i00002-22i−2i22−2−2-2-222−2i−2i2i2ii2i2−i2−i2002−2i2−i20000−2−222−i2−i2i2i20000000000000000ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000
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χ442-22-22i2i−2i−2i00002-22i−2i−2−222-2-222−2i−2i2i2i−i2−i2i2i200−22−i2i2000022−2−2i2i2−i2−i20000000000000000−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000
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χ462-22-2−2i−2i2i2i00002-2−2i2i22−2−222-2-2−2i−2i2i2i−i2−i2i2i2002−2−i2i2000022−2−2−i2−i2i2i20000000000000000−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000
χ472-22-2−2i−2i2i2i00002-2−2i2i22−2−2-2-2222i2i−2i−2i−i2−i2i2i2002−2−i2i20000−2−222i2i2−i2−i20000000000000000ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000
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χ522-22-2−2i−2i2i2i00002-2−2i2i−2−222-2-2222i2i−2i−2ii2i2−i2−i200−22i2−i2000022−2−2−i2−i2i2i20000000000000000−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000
χ532-2-222i−2i2i−2i2i−2i2-200002-22-22−22−2i2−i2i2−i22i−2i2i−2i0000002−2i2−i22−22−2i2−i2i2−i2002ζ6−2ζ6002ζ2−2ζ21−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
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χ854-4-44−4i4i−4i4i4i−4i-440000000022−2222−22−2i22i2−2i22i20000000000−22222i2−2i200000000000000000000000000000000000000000000
χ864-4-44−4i4i−4i4i4i−4i-4400000000−2222−22222i2−2i22i2−2i2000000000022−22−2i22i200000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.