Finite Group Databasebeta

← Group #138285

Character table — Group #138285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222222222444444444444888888884444448888888888884444444444444444161616161616161616161616161616162444
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
χ511111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11
χ611111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1
χ711111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111-1
χ811111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-11
χ911111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ1011111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111
χ1111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111
χ1211111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1
χ1411111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-11
χ1511111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-11
χ1611111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ19222222222222-2-222222222-2-200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ20222222222222-2-222222222-2-200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-2-2-2-2222222-2-2-2-22222222222-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-222222222222222-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-20000000022-2-2220000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-20000000022-2-2220000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002222-2-20000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002222-2-20000000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000
χ29222-2-2-2-222-22-2002i2i−2i−2i2i2i−2i−2i002222−2−2−2−200000022−2−2i2i2−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
χ30222-2-2-2-222-22-2002i2i−2i−2i2i2i−2i−2i002222−2−2−2−200000022−2−2i2i2−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
χ31222-2-2-2-222-22-2002i2i−2i−2i2i2i−2i−2i00−2−2−2−22222000000−2−222−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
χ32222-2-2-2-222-22-2002i2i−2i−2i2i2i−2i−2i00−2−2−2−22222000000−2−222−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
χ33222-2-2-2-222-22-200−2i−2i2i2i−2i−2i2i2i002222−2−2−2−200000022−2−2−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
χ34222-2-2-2-222-22-200−2i−2i2i2i−2i−2i2i2i002222−2−2−2−200000022−2−2−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
χ35222-2-2-2-222-22-200−2i−2i2i2i−2i−2i2i2i00−2−2−2−22222000000−2−222i2i2−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
χ36222-2-2-2-222-22-200−2i−2i2i2i−2i−2i2i2i00−2−2−2−22222000000−2−222i2i2−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
χ37222-2-2-2-22-22-22002i2i−2i−2i−2i−2i2i2i002222−2−2−2−2000000−2−222−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
χ38222-2-2-2-22-22-22002i2i−2i−2i−2i−2i2i2i002222−2−2−2−2000000−2−222−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
χ39222-2-2-2-22-22-22002i2i−2i−2i−2i−2i2i2i00−2−2−2−2222200000022−2−2i2i2−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
χ40222-2-2-2-22-22-22002i2i−2i−2i−2i−2i2i2i00−2−2−2−2222200000022−2−2i2i2−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
χ41222-2-2-2-22-22-2200−2i−2i2i2i2i2i−2i−2i002222−2−2−2−2000000−2−222i2i2−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
χ42222-2-2-2-22-22-2200−2i−2i2i2i2i2i−2i−2i002222−2−2−2−2000000−2−222i2i2−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
χ43222-2-2-2-22-22-2200−2i−2i2i2i2i2i−2i−2i00−2−2−2−2222200000022−2−2−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
χ44222-2-2-2-22-22-2200−2i−2i2i2i2i2i−2i−2i00−2−2−2−2222200000022−2−2−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
χ4522-22-22-2-200002-200002i−2i2i−2i2-22i2i−2i−2i2i2i−2i−2i00002i−2i00002-22-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ4622-22-22-2-200002-200002i−2i2i−2i2-22i2i−2i−2i2i2i−2i−2i00002i−2i00002-22-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ4722-22-22-2-200002-200002i−2i2i−2i2-2−2i−2i2i2i−2i−2i2i2i00002i−2i0000-22-2200001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ4822-22-22-2-200002-200002i−2i2i−2i2-2−2i−2i2i2i−2i−2i2i2i00002i−2i0000-22-220000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ4922-22-22-2-200002-20000−2i2i−2i2i2-22i2i−2i−2i2i2i−2i−2i0000−2i2i0000-22-2200001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ5022-22-22-2-200002-20000−2i2i−2i2i2-22i2i−2i−2i2i2i−2i−2i0000−2i2i0000-22-220000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ5122-22-22-2-200002-20000−2i2i−2i2i2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i00002-22-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ5222-22-22-2-200002-20000−2i2i−2i2i2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i00002-22-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ532-222-2-22-20000-222i−2i2i−2i00002-22i−2i2i−2i2i−2i2i−2i002i−2i00000000002-22-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ542-222-2-22-20000-222i−2i2i−2i00002-22i−2i2i−2i2i−2i2i−2i002i−2i00000000002-22-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ552-222-2-22-20000-222i−2i2i−2i00002-2−2i2i−2i2i−2i2i−2i2i002i−2i0000000000-22-221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ562-222-2-22-20000-222i−2i2i−2i00002-2−2i2i−2i2i−2i2i−2i2i002i−2i0000000000-22-22−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ572-222-2-22-20000-22−2i2i−2i2i00002-22i−2i2i−2i2i−2i2i−2i00−2i2i0000000000-22-221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ582-222-2-22-20000-22−2i2i−2i2i00002-22i−2i2i−2i2i−2i2i−2i00−2i2i0000000000-22-22−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ592-222-2-22-20000-22−2i2i−2i2i00002-2−2i2i−2i2i−2i2i−2i2i00−2i2i00000000002-22-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ602-222-2-22-20000-22−2i2i−2i2i00002-2−2i2i−2i2i−2i2i−2i2i00−2i2i00000000002-22-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ612-2-222-2-2222-2-2-2-200000000222-2-222-2-222-200002-22-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ622-2-222-2-2222-2-2-2-200000000222-2-222-2-222-200002-22-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ632-2-222-2-2222-2-2-2-20000000022-222-2-222-22-20000-22-22000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ642-2-222-2-2222-2-2-2-20000000022-222-2-222-22-20000-22-2200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ652-2-222-2-22-2-222-2-200000000222-2-222-2-22-220000-22-22000000002-2-222-2-220000000000000000000000000000
χ662-2-222-2-22-2-222-2-200000000222-2-222-2-22-220000-22-2200000000-222-2-222-20000000000000000000000000000
χ672-2-222-2-22-2-222-2-20000000022-222-2-222-2-2200002-22-200000000000000002-2-222-2-2200000000000000000000
χ682-2-222-2-22-2-222-2-20000000022-222-2-222-2-2200002-22-20000000000000000-222-2-222-200000000000000000000
χ6944-44-44-4-40000-4400004i−4i4i−4i-44000000000000−4i4i000000000000000000000000000000000000000000000000
χ7044-44-44-4-40000-440000−4i4i−4i4i-440000000000004i−4i000000000000000000000000000000000000000000000000
χ7144-4-44-44-400000000004-4-44002i22i2−2i2−2i2−2i2−2i22i22i20000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ7244-4-44-44-400000000004-4-4400−2i2−2i22i22i22i22i2−2i2−2i200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ7344-4-44-44-40000000000-444-4002i22i2−2i2−2i2−2i2−2i22i22i200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ7444-4-44-44-40000000000-444-400−2i2−2i22i22i22i22i2−2i2−2i20000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ754-444-4-44-400004-44i−4i4i−4i0000-440000000000−4i4i00000000000000000000000000000000000000000000000000
χ764-444-4-44-400004-4−4i4i−4i4i0000-4400000000004i−4i00000000000000000000000000000000000000000000000000
χ774-44-444-4-40000004-4-440000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ784-44-444-4-40000004-4-44000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ794-44-444-4-4000000-444-40000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ804-44-444-4-4000000-444-4000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ814-4-444-4-4444-4-44400000000-4-400000000-440000000000000000000000000000000000000000000000000000
χ824-4-444-4-44-4-4444400000000-4-4000000004-40000000000000000000000000000000000000000000000000000
χ834-4-4-4-44444-4-4400000000000022−22−2222−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ844-4-4-4-44444-4-44000000000000−222222−2222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ854-4-4-4-4444-444-400000000000022−22−2222−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ864-4-4-4-4444-444-4000000000000−222222−2222−22−222200000022−22−222200000000000000000000000000000000000000000000

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