Finite Group Databasebeta

← Group #138249

Character table — Group #138249

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222222222444444444444888888882222448888888888884444444444444444161616161616161616161616161616162444
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
χ5111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ1011111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ1111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ1211111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ1311111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11
χ1411111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ1511111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ1611111111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ18222222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222000000000000000000000000000000000000
χ19222222222222-2-2-222222222-200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ20222222222222-2-2-222222222-200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-2000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-2-2-2-22222222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22222222222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2-200000000-2-222220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-200000000-2-222220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-20000000022-2-2220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-20000000022-2-2220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000
χ29222-22-2-2-22-22-20002i2i−2i−2i2i2i−2i−2i02222−2−2−2−200000022−2−2i2i2−i2−i2i2i2−i2−i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ30222-22-2-2-22-22-20002i2i−2i−2i2i2i−2i−2i02222−2−2−2−200000022−2−2i2i2−i2−i2i2i2−i2−i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ31222-22-2-2-22-22-20002i2i−2i−2i2i2i−2i−2i0−2−2−2−22222000000−2−222−i2−i2i2i2−i2−i2i2i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ32222-22-2-2-22-22-20002i2i−2i−2i2i2i−2i−2i0−2−2−2−22222000000−2−222−i2−i2i2i2−i2−i2i2i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ33222-22-2-2-22-22-2000−2i−2i2i2i−2i−2i2i2i02222−2−2−2−200000022−2−2−i2−i2i2i2−i2−i2i2i20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000
χ34222-22-2-2-22-22-2000−2i−2i2i2i−2i−2i2i2i02222−2−2−2−200000022−2−2−i2−i2i2i2−i2−i2i2i20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000
χ35222-22-2-2-22-22-2000−2i−2i2i2i−2i−2i2i2i0−2−2−2−22222000000−2−222i2i2−i2−i2i2i2−i2−i20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000
χ36222-22-2-2-22-22-2000−2i−2i2i2i−2i−2i2i2i0−2−2−2−22222000000−2−222i2i2−i2−i2i2i2−i2−i20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000
χ37222-22-2-2-2-22-220002i2i−2i−2i−2i−2i2i2i02222−2−2−2−2000000−2−222−i2−i2i2i2i2i2−i2−i20000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ38222-22-2-2-2-22-220002i2i−2i−2i−2i−2i2i2i02222−2−2−2−2000000−2−222−i2−i2i2i2i2i2−i2−i20000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ39222-22-2-2-2-22-220002i2i−2i−2i−2i−2i2i2i0−2−2−2−2222200000022−2−2i2i2−i2−i2−i2−i2i2i20000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ40222-22-2-2-2-22-220002i2i−2i−2i−2i−2i2i2i0−2−2−2−2222200000022−2−2i2i2−i2−i2−i2−i2i2i20000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ41222-22-2-2-2-22-22000−2i−2i2i2i2i2i−2i−2i02222−2−2−2−2000000−2−222i2i2−i2−i2−i2−i2i2i20000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ42222-22-2-2-2-22-22000−2i−2i2i2i2i2i−2i−2i02222−2−2−2−2000000−2−222i2i2−i2−i2−i2−i2i2i20000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ43222-22-2-2-2-22-22000−2i−2i2i2i2i2i−2i−2i0−2−2−2−2222200000022−2−2−i2−i2i2i2i2i2−i2−i20000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ44222-22-2-2-2-22-22000−2i−2i2i2i2i2i−2i−2i0−2−2−2−2222200000022−2−2−i2−i2i2i2i2i2−i2−i20000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ4522-2-2-222-2000022-200002-22-2-22i2i−2i−2i2i2i−2i−2i002-20000002i−2i2i−2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ4622-2-2-222-2000022-200002-22-2-22i2i−2i−2i2i2i−2i−2i002-20000002i−2i2i−2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ4722-2-2-222-2000022-200002-22-2-2−2i−2i2i2i−2i−2i2i2i002-2000000−2i2i−2i2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ4822-2-2-222-2000022-200002-22-2-2−2i−2i2i2i−2i−2i2i2i002-2000000−2i2i−2i2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ4922-2-2-222-2000022-20000-22-22-22i2i−2i−2i2i2i−2i−2i00-22000000−2i2i−2i2i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ5022-2-2-222-2000022-20000-22-22-22i2i−2i−2i2i2i−2i−2i00-22000000−2i2i−2i2i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ5122-2-2-222-2000022-20000-22-22-2−2i−2i2i2i−2i−2i2i2i00-220000002i−2i2i−2i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ5222-2-2-222-2000022-20000-22-22-2−2i−2i2i2i−2i−2i2i2i00-220000002i−2i2i−2i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ532-22-2-22-2200002-222-22-20000-22i−2i2i−2i2i−2i2i−2i2-20000000000002i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ542-22-2-22-2200002-222-22-20000-22i−2i2i−2i2i−2i2i−2i2-20000000000002i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ552-22-2-22-2200002-222-22-20000-2−2i2i−2i2i−2i2i−2i2i2-2000000000000−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
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χ572-22-2-22-2200002-22-22-220000-22i−2i2i−2i2i−2i2i−2i-22000000000000−2i2i−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
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χ592-22-2-22-2200002-22-22-220000-2−2i2i−2i2i−2i2i−2i2i-220000000000002i−2i2i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ602-22-2-22-2200002-22-22-220000-2−2i2i−2i2i−2i2i−2i2i-220000000000002i−2i2i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
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χ642-2-2222-2-222-2-22-2-2000000002-222-2-222-200002-2-22-2200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ652-2-2222-2-2-2-2222-2-20000000022-2-222-2-220000-22-22-22000000002-2-222-2-220000000000000000000000000000
χ662-2-2222-2-2-2-2222-2-20000000022-2-222-2-220000-22-22-2200000000-222-2-222-20000000000000000000000000000
χ672-2-2222-2-2-2-2222-2-2000000002-222-2-222-20000-222-22-200000000000000002-2-222-2-2200000000000000000000
χ682-2-2222-2-2-2-2222-2-2000000002-222-2-222-20000-222-22-20000000000000000-222-2-222-200000000000000000000
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χ7344-4-4-444-40000-4-4400004-44-440000000000-4400000000000000000000000000000000000000000000000000
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χ774-444-4-44-40000000−4i4i4i−4i000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000022−22−2222000000000000000000000000000000000000
χ784-444-4-44-40000000−4i4i4i−4i00000−2i22i2−2i22i22i2−2i22i2−2i200000000000000−222222−22000000000000000000000000000000000000
χ794-44-4-44-440000-44-44-44-40000400000000-440000000000000000000000000000000000000000000000000000
χ804-44-4-44-440000-44-4-44-4400004000000004-40000000000000000000000000000000000000000000000000000
χ814-4-4444-4-444-4-4-44400000000-4000000000000-44000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-4-444-44400000000-40000000000004-4000000000000000000000000000000000000000000000000
χ834-4-4-44-4444-4-4400000000000022−22−2222−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ844-4-4-44-4444-4-44000000000000−222222−2222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ854-4-4-44-444-444-400000000000022−22−2222−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ864-4-4-44-444-444-4000000000000−222222−2222−22−222200000022−22−222200000000000000000000000000000000000000000000

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