Finite Group Databasebeta

← Group #138129

Character table — Group #138129

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222224444444444444444888888882244448888888888888888888888888888161616161616161616161616161616164444
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
χ511111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-1
χ611111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-11
χ711111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-11
χ811111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-11-1
χ91111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-11
χ101111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1
χ111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1
χ121111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1-11
χ131111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ141111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ151111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ161111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ192222222222-2-2-2-22222-2-222-2-222222222-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-222222222000000000000000000000000000000000000
χ2122222222-2-22222222222-2-22200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ2222222222-2-22222222222-2-22200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-2000000002222-2-20000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2000000002222-2-20000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2220000000022-2-222000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2220000000022-2-2220000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ29222-22-2-2-22-222-2-20000002-2002222-2-2-2-22-200000000000022-2-222−2−222−2−222−2−222−2−200000000000000000000
χ30222-22-2-2-22-222-2-20000002-2002222-2-2-2-22-200000000000022-2-2−2−222−2−222−2−222−2−22200000000000000000000
χ31222-22-2-2-22-222-2-20000002-200-2-2-2-222222-2000000000000-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000
χ32222-22-2-2-22-222-2-20000002-200-2-2-2-222222-2000000000000-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000
χ33222-22-2-2-22-2-2-2220000002-2002222-2-2-2-2-22000000000000-2-22222−2−2−2−222−2−22222−2−200000000000000000000
χ34222-22-2-2-22-2-2-2220000002-2002222-2-2-2-2-22000000000000-2-222−2−22222−2−222−2−2−2−22200000000000000000000
χ35222-22-2-2-22-2-2-2220000002-200-2-2-2-22222-2200000000000022-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000
χ36222-22-2-2-22-2-2-2220000002-200-2-2-2-22222-2200000000000022-2-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000
χ3722-22-2-2-22002i−2i2i−2i2i2i−2i−2i2-2002-222−2−222−2−200000022−2−2i2i2−i2−i2i2−i2i2−i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ3822-22-2-2-22002i−2i2i−2i2i2i−2i−2i2-2002-222−2−222−2−200000022−2−2i2i2−i2−i2i2−i2i2−i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ3922-22-2-2-22002i−2i2i−2i2i2i−2i−2i2-2002-2−2−222−2−222000000−2−222−i2−i2i2i2−i2i2−i2i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ4022-22-2-2-22002i−2i2i−2i2i2i−2i−2i2-2002-2−2−222−2−222000000−2−222−i2−i2i2i2−i2i2−i2i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ4122-22-2-2-22002i−2i2i−2i−2i−2i2i2i-2200-2222−2−222−2−2000000−2−222−i2−i2i2i2i2−i2i2−i20000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ4222-22-2-2-22002i−2i2i−2i−2i−2i2i2i-2200-2222−2−222−2−2000000−2−222−i2−i2i2i2i2−i2i2−i20000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ4322-22-2-2-22002i−2i2i−2i−2i−2i2i2i-2200-22−2−222−2−22200000022−2−2i2i2−i2−i2−i2i2−i2i20000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ4422-22-2-2-22002i−2i2i−2i−2i−2i2i2i-2200-22−2−222−2−22200000022−2−2i2i2−i2−i2−i2i2−i2i20000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ4522-22-2-2-2200−2i2i−2i2i2i2i−2i−2i-2200-2222−2−222−2−2000000−2−222i2i2−i2−i2−i2i2−i2i20000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ4622-22-2-2-2200−2i2i−2i2i2i2i−2i−2i-2200-2222−2−222−2−2000000−2−222i2i2−i2−i2−i2i2−i2i20000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ4722-22-2-2-2200−2i2i−2i2i2i2i−2i−2i-2200-22−2−222−2−22200000022−2−2−i2−i2i2i2i2−i2i2−i20000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ4822-22-2-2-2200−2i2i−2i2i2i2i−2i−2i-2200-22−2−222−2−22200000022−2−2−i2−i2i2i2i2−i2i2−i20000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ4922-22-2-2-2200−2i2i−2i2i−2i−2i2i2i2-2002-222−2−222−2−200000022−2−2−i2−i2i2i2−i2i2−i2i20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ5022-22-2-2-2200−2i2i−2i2i−2i−2i2i2i2-2002-222−2−222−2−200000022−2−2−i2−i2i2i2−i2i2−i2i20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ5122-22-2-2-2200−2i2i−2i2i−2i−2i2i2i2-2002-2−2−222−2−222000000−2−222i2i2−i2−i2i2−i2i2−i20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ5222-22-2-2-2200−2i2i−2i2i−2i−2i2i2i2-2002-2−2−222−2−222000000−2−222i2i2−i2−i2i2−i2i2−i20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ532-2-222-22-2-2200002i−2i2i−2i002-2002-22-22-22-200002i−2i00002i−2i2i−2i0000i2−i2i2−i22−22−22−22−2i2−i2i2−i200000000000000000000
χ542-2-222-22-2-2200002i−2i2i−2i002-2002-22-22-22-200002i−2i00002i−2i2i−2i0000−i2i2−i2i2−22−22−22−22−i2i2−i2i200000000000000000000
χ552-2-222-22-2-2200002i−2i2i−2i002-200-22-22-22-2200002i−2i0000−2i2i−2i2i00002−22−2i2−i2i2−i2−i2i2−i2i2−22−2200000000000000000000
χ562-2-222-22-2-2200002i−2i2i−2i002-200-22-22-22-2200002i−2i0000−2i2i−2i2i0000−22−22−i2i2−i2i2i2−i2i2−i22−22−200000000000000000000
χ572-2-222-22-2-220000−2i2i−2i2i002-2002-22-22-22-20000−2i2i0000−2i2i−2i2i0000i2−i2i2−i2−22−22−22−22i2−i2i2−i200000000000000000000
χ582-2-222-22-2-220000−2i2i−2i2i002-2002-22-22-22-20000−2i2i0000−2i2i−2i2i0000−i2i2−i2i22−22−22−22−2−i2i2−i2i200000000000000000000
χ592-2-222-22-2-220000−2i2i−2i2i002-200-22-22-22-220000−2i2i00002i−2i2i−2i00002−22−2−i2i2−i2i2i2−i2i2−i2−22−2200000000000000000000
χ602-2-222-22-2-220000−2i2i−2i2i002-200-22-22-22-220000−2i2i00002i−2i2i−2i0000−22−22i2−i2i2−i2−i2i2−i2i22−22−200000000000000000000
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χ642-2-2-222-22-2-2000000002222-2-2-22-222-22-2002-200-22-22000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ652-2-2-222-22-2-200000000-2-222222-22-2-22-2200-2200-22-220000000000002-2-222-2-22000000000000000000000000
χ662-2-2-222-22-2-200000000-2-222222-22-2-22-2200-2200-22-22000000000000-222-2-222-2000000000000000000000000
χ672-2-2-222-22-2-200000000-2-22222-22-222-22-200-22002-22-2000000002-2-2200000000-222-200000000000000000000
χ682-2-2-222-22-2-200000000-2-22222-22-222-22-200-22002-22-200000000-222-2000000002-2-2200000000000000000000
χ69444-44-4-4-4-4444-4-4000000-440000000000-440000000000000000000000000000000000000000000000000000
χ70444-44-4-4-4-44-4-444000000-4400000000004-40000000000000000000000000000000000000000000000000000
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χ7344-4-4-444-400−4i4i4i−4i00000000002222−22−22−22−22222200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
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χ754-444-44-4-40000004-4-4400000022−22−222222−22−2222000000000022−22−22220000000000000000000000000000000000000000
χ764-444-44-4-40000004-4-44000000−222222−22−222222−220000000000−222222−220000000000000000000000000000000000000000
χ774-444-44-4-4000000-444-400000022−22−222222−22−22220000000000−222222−220000000000000000000000000000000000000000
χ784-444-44-4-4000000-444-4000000−222222−22−222222−22000000000022−22−22220000000000000000000000000000000000000000
χ794-44-4-4-44400000000004-400-4422−22−2222−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ804-44-4-4-44400000000004-400-44−222222−2222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ814-44-4-4-4440000000000-44004-422−22−2222−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ824-44-4-4-4440000000000-44004-4−222222−2222−22−222200000022−22−222200000000000000000000000000000000000000000000
χ834-4-444-44-44-400004i−4i4i−4i00-4400000000000000−4i4i000000000000000000000000000000000000000000000000
χ844-4-444-44-44-40000−4i4i−4i4i00-44000000000000004i−4i000000000000000000000000000000000000000000000000
χ854-4-4-444-44440000000044-4-4-4-40000000000-4400000000000000000000000000000000000000000000000000
χ864-4-4-444-444400000000-4-4-4-44400000000004-400000000000000000000000000000000000000000000000000

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