Finite Group Databasebeta

← Group #138284

Character table — Group #138284

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
χ2922-22-22-2-200002-200002i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i00002i−2i000022-2-200001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ3022-22-22-2-200002-200002i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i00002i−2i000022-2-20000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ3122-22-22-2-200002-200002i2i−2i−2i2-2−2i−2i−2i−2i2i2i2i2i00002i−2i0000-2-22200001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ3222-22-22-2-200002-200002i2i−2i−2i2-2−2i−2i−2i−2i2i2i2i2i00002i−2i0000-2-2220000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ3322-22-22-2-200002-20000−2i−2i2i2i2-22i2i2i2i−2i−2i−2i−2i0000−2i2i0000-2-22200001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000
χ3422-22-22-2-200002-20000−2i−2i2i2i2-22i2i2i2i−2i−2i−2i−2i0000−2i2i0000-2-2220000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000000000
χ3522-22-22-2-200002-20000−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i000022-2-200001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000000000
χ3622-22-22-2-200002-20000−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i0000−2i2i000022-2-20000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000000000
χ372-222-2-22-20000-222i2i−2i−2i00002-22i2i−2i−2i2i2i−2i−2i002i−2i000000000022-2-21+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ382-222-2-22-20000-222i2i−2i−2i00002-22i2i−2i−2i2i2i−2i−2i002i−2i000000000022-2-2−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ392-222-2-22-20000-222i2i−2i−2i00002-2−2i−2i2i2i−2i−2i2i2i002i−2i0000000000-2-2221−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ402-222-2-22-20000-222i2i−2i−2i00002-2−2i−2i2i2i−2i−2i2i2i002i−2i0000000000-2-222−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ412-222-2-22-20000-22−2i−2i2i2i00002-22i2i−2i−2i2i2i−2i−2i00−2i2i0000000000-2-2221+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ422-222-2-22-20000-22−2i−2i2i2i00002-22i2i−2i−2i2i2i−2i−2i00−2i2i0000000000-2-222−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000
χ432-222-2-22-20000-22−2i−2i2i2i00002-2−2i−2i2i2i−2i−2i2i2i00−2i2i000000000022-2-21−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ442-222-2-22-20000-22−2i−2i2i2i00002-2−2i−2i2i2i−2i−2i2i2i00−2i2i000000000022-2-2−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ452-2-222-2-2222-2-2-2-2000000002222-2-2-2-2222-2000022-2-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ462-2-222-2-2222-2-2-2-2000000002222-2-2-2-2222-2000022-2-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ472-2-222-2-2222-2-2-2-20000000022-2-22222-2-22-20000-2-222000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ482-2-222-2-2222-2-2-2-20000000022-2-22222-2-22-20000-2-22200000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ492-2-222-2-22-2-222-2-2000000002222-2-2-2-222-220000-2-222000000002-2-222-2-220000000000000000000000000000
χ502-2-222-2-22-2-222-2-2000000002222-2-2-2-222-220000-2-22200000000-222-2-222-20000000000000000000000000000
χ512-2-222-2-22-2-222-2-20000000022-2-22222-2-2-22000022-2-200000000000000002-2-222-2-2200000000000000000000
χ522-2-222-2-22-2-222-2-20000000022-2-22222-2-2-22000022-2-20000000000000000-222-2-222-200000000000000000000
χ532-2-2-2-22222-22-2002-22-22-22-2002−22−22−22−20000002−22−22−22−22−22−20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ542-2-2-2-22222-22-2002-22-22-22-2002−22−22−22−20000002−22−22−22−22−22−20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ552-2-2-2-22222-22-2002-22-22-22-200−22−22−22−22000000−22−22−22−22−22−220000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ562-2-2-2-22222-22-2002-22-22-22-200−22−22−22−22000000−22−22−22−22−22−220000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ572-2-2-2-22222-22-200-22-22-22-22002−22−22−22−20000002−22−2−22−22−22−220000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ582-2-2-2-22222-22-200-22-22-22-22002−22−22−22−20000002−22−2−22−22−22−220000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ592-2-2-2-22222-22-200-22-22-22-2200−22−22−22−22000000−22−222−22−22−22−20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ602-2-2-2-22222-22-200-22-22-22-2200−22−22−22−22000000−22−222−22−22−22−20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ612-2-2-2-2222-22-22002-22-2-22-22002−22−22−22−2000000−22−22−22−222−22−20000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ622-2-2-2-2222-22-22002-22-2-22-22002−22−22−22−2000000−22−22−22−222−22−20000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ632-2-2-2-2222-22-22002-22-2-22-2200−22−22−22−220000002−22−22−22−2−22−220000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ642-2-2-2-2222-22-22002-22-2-22-2200−22−22−22−220000002−22−22−22−2−22−220000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ652-2-2-2-2222-22-2200-22-222-22-2002−22−22−22−2000000−22−222−22−2−22−220000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ662-2-2-2-2222-22-2200-22-222-22-2002−22−22−22−2000000−22−222−22−2−22−220000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ672-2-2-2-2222-22-2200-22-222-22-200−22−22−22−220000002−22−2−22−222−22−20000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ682-2-2-2-2222-22-2200-22-222-22-200−22−22−22−220000002−22−2−22−222−22−20000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ69444-4-4-4-444-4-4400000000000022−22−2222−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ70444-4-4-4-444-4-44000000000000−222222−2222−22−2222000000−222222−2200000000000000000000000000000000000000000000
χ71444-4-4-4-44-444-400000000000022−22−2222−222222−22000000−222222−2200000000000000000000000000000000000000000000
χ72444-4-4-4-44-444-4000000000000−222222−2222−22−222200000022−22−222200000000000000000000000000000000000000000000
χ7344-44-44-4-40000-4400004i4i−4i−4i-44000000000000−4i4i000000000000000000000000000000000000000000000000
χ7444-44-44-4-40000-440000−4i−4i4i4i-440000000000004i−4i000000000000000000000000000000000000000000000000
χ7544-4-44-44-40000004i−4i−4i4i0000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000022−22−2222000000000000000000000000000000000000
χ7644-4-44-44-40000004i−4i−4i4i000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−222222−22000000000000000000000000000000000000
χ7744-4-44-44-4000000−4i4i4i−4i0000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−222222−22000000000000000000000000000000000000
χ7844-4-44-44-4000000−4i4i4i−4i000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000022−22−2222000000000000000000000000000000000000
χ794-444-4-44-400004-44i4i−4i−4i0000-440000000000−4i4i00000000000000000000000000000000000000000000000000
χ804-444-4-44-400004-4−4i−4i4i4i0000-4400000000004i−4i00000000000000000000000000000000000000000000000000
χ814-44-444-4-400000000004i−4i−4i4i002i2−2i22i2−2i2−2i22i2−2i22i2000000000022−22−22220000000000000000000000000000000000000000
χ824-44-444-4-400000000004i−4i−4i4i00−2i22i2−2i22i22i2−2i22i2−2i20000000000−222222−220000000000000000000000000000000000000000
χ834-44-444-4-40000000000−4i4i4i−4i002i2−2i22i2−2i2−2i22i2−2i22i20000000000−222222−220000000000000000000000000000000000000000
χ844-44-444-4-40000000000−4i4i4i−4i00−2i22i2−2i22i22i2−2i22i2−2i2000000000022−22−22220000000000000000000000000000000000000000
χ854-4-444-4-4444-4-44400000000-4-400000000-440000000000000000000000000000000000000000000000000000
χ864-4-444-4-44-4-4444400000000-4-4000000004-40000000000000000000000000000000000000000000000000000

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