Finite Group Databasebeta

← Group #138138

Character table — Group #138138

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222222222444444444444888888884444448888888888888888888888888888161616161616161616161616161616162444
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
χ5111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1
χ6111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111
χ7111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111
χ8111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1
χ911111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ1011111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ1111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ1211111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ1311111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11
χ1411111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1611111111-1-1-1-1-1-1-1-11111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ18222222222222222222-2-2-2-22200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ19222222222222222222-2-2-2-22200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ20222222222222-2-2-2-2-2-22222-2-222222222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-20000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000
χ2322222222-2-2-2-22222-2-22222-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ2622222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222222222000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-2220000000022-2-222000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-2220000000022-2-2220000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ29222-2-2-2-2200002i2i−2i−2i002-22-20022-2-222-2-22i−2i000000002i2i−2i−2i0000i2i2−i2−i222−2−222−2−2i2i2−i2−i200000000000000000000
χ30222-2-2-2-2200002i2i−2i−2i002-22-20022-2-222-2-22i−2i000000002i2i−2i−2i0000−i2−i2i2i2−2−222−2−222−i2−i2i2i200000000000000000000
χ31222-2-2-2-2200002i2i−2i−2i002-22-200-2-222-2-2222i−2i00000000−2i−2i2i2i000022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000000000
χ32222-2-2-2-2200002i2i−2i−2i002-22-200-2-222-2-2222i−2i00000000−2i−2i2i2i0000−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000000000
χ33222-2-2-2-220000−2i−2i2i2i002-22-20022-2-222-2-2−2i2i00000000−2i−2i2i2i0000i2i2−i2−i2−2−222−2−222i2i2−i2−i200000000000000000000
χ34222-2-2-2-220000−2i−2i2i2i002-22-20022-2-222-2-2−2i2i00000000−2i−2i2i2i0000−i2−i2i2i222−2−222−2−2−i2−i2i2i200000000000000000000
χ35222-2-2-2-220000−2i−2i2i2i002-22-200-2-222-2-222−2i2i000000002i2i−2i−2i000022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000000000
χ36222-2-2-2-220000−2i−2i2i2i002-22-200-2-222-2-222−2i2i000000002i2i−2i−2i0000−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000000000
χ3722-22-22-2-222-2-22i−2i2i−2i2i−2i00002i−2ii2−i2i2−i2i2−i2i2−i200000022−2−22−22−2i2i2−i2−i20000000000000000ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000
χ3822-22-22-2-222-2-22i−2i2i−2i2i−2i00002i−2ii2−i2i2−i2i2−i2i2−i200000022−2−22−22−2i2i2−i2−i20000000000000000−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000
χ3922-22-22-2-222-2-22i−2i2i−2i2i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2000000−2−222−22−22−i2−i2i2i20000000000000000ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000
χ4022-22-22-2-222-2-22i−2i2i−2i2i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2000000−2−222−22−22−i2−i2i2i20000000000000000−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000
χ4122-22-22-2-222-2-2−2i2i−2i2i−2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2000000−2−222−22−22i2i2−i2−i20000000000000000ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000
χ4222-22-22-2-222-2-2−2i2i−2i2i−2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2000000−2−222−22−22i2i2−i2−i20000000000000000−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000
χ4322-22-22-2-222-2-2−2i2i−2i2i−2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i200000022−2−22−22−2−i2−i2i2i20000000000000000ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000
χ4422-22-22-2-222-2-2−2i2i−2i2i−2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i200000022−2−22−22−2−i2−i2i2i20000000000000000−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000
χ4522-22-22-2-2-2-2222i−2i2i−2i−2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2000000−2−2222−22−2−i2−i2i2i20000000000000000ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000
χ4622-22-22-2-2-2-2222i−2i2i−2i−2i2i0000−2i2ii2−i2i2−i2i2−i2i2−i2000000−2−2222−22−2−i2−i2i2i20000000000000000−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000
χ4722-22-22-2-2-2-2222i−2i2i−2i−2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i200000022−2−2−22−22i2i2−i2−i20000000000000000ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000
χ4822-22-22-2-2-2-2222i−2i2i−2i−2i2i0000−2i2i−i2i2−i2i2−i2i2−i2i200000022−2−2−22−22i2i2−i2−i20000000000000000−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000
χ4922-22-22-2-2-2-222−2i2i−2i2i2i−2i00002i−2ii2−i2i2−i2i2−i2i2−i200000022−2−2−22−22−i2−i2i2i20000000000000000ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000
χ5022-22-22-2-2-2-222−2i2i−2i2i2i−2i00002i−2ii2−i2i2−i2i2−i2i2−i200000022−2−2−22−22−i2−i2i2i20000000000000000−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000
χ5122-22-22-2-2-2-222−2i2i−2i2i2i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2000000−2−2222−22−2i2i2−i2−i20000000000000000ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000
χ5222-22-22-2-2-2-222−2i2i−2i2i2i−2i00002i−2i−i2i2−i2i2−i2i2−i2i2000000−2−2222−22−2i2i2−i2−i20000000000000000−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000
χ532-2-222-2-220000000022-2-222-2-222-2-2-2-222002-2002-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ542-2-222-2-220000000022-2-222-2-222-2-2-2-222002-2002-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ552-2-222-2-220000000022-2-222-2-2-2-22222-2-2002-200-22-22000000002i−2i2i−2i000000002i−2i2i−2i00000000000000000000
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χ642-2-2-2-22222-22-2000000-222-200-2-2-2-2222200002-200000000-22-22−222−2−222−22−2−22−222−200000000000000000000
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χ662-2-2-2-2222-22-22000000-222-2002222-2-2-2-20000-2200000000-22-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000000000
χ672-2-2-2-2222-22-22000000-222-200-2-2-2-222220000-22000000002-22-22−2−22−222−22−2−222−2−2200000000000000000000
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χ814-44-444-4-4-444-40000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ824-44-444-4-4-444-4000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ834-4-444-4-44000000004444-4-4-4-40000000000-4400000000000000000000000000000000000000000000000000
χ844-4-444-4-4400000000-4-444-4-44400000000004-400000000000000000000000000000000000000000000000000
χ854-4-4-4-44444-44-40000004-4-4400000000000000-44000000000000000000000000000000000000000000000000
χ864-4-4-4-4444-44-440000004-4-44000000000000004-4000000000000000000000000000000000000000000000000

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