Finite Group Databasebeta

← Group #141249

Character table — Group #141249

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222224444444488888888888888884488888888888888884444444488888888161616161616161616161616161616162244
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
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91-1-111-1-11-1-1-11111-11111-1-11111-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1
χ101-1-111-1-11-1-1-11111-11111-1-11111-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-11
χ111-1-111-1-11-1-1-11111-11111-1-11111-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-11
χ121-1-111-1-11-1-1-11111-11111-1-11111-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ131-1-111-1-11-1-1-11111-11111-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11
χ141-1-111-1-11-1-1-11111-11111-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ151-1-111-1-11-1-1-11111-11111-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ161-1-111-1-11-1-1-11111-11111-1-1-1-1-1-11111-1-1-1111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ172222222222222222-2-2-2-2-2-222222222-2-222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ19222222222-2-222-2-220000002222222200-2-20000-2-2-2-200000000000000000000000022−2−222−2−222−2−222−2−20000
χ20222222222-2-222-2-220000002222222200-2-20000-2-2-2-2000000000000000000000000−2−222−2−222−2−222−2−2220000
χ21222222222-2-222-2-22000000-2-2-2-2-2-2-2-200-2-20000222200000000000000000000000022−2−222−2−2−2−222−2−2220000
χ22222222222-2-222-2-22000000-2-2-2-2-2-2-2-200-2-200002222000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-222-2-222-22222220000000022-2-2-2-2-2-200000000000022-2-222-2-20000000000000000000000000000
χ2422222222-222-2-222-22222220000000022-2-2-2-2-2-2000000000000-2-222-2-2220000000000000000000000000000
χ2522222222-222-2-222-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222-222-2-222-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ272222-2-2-2-2-2002-200222−2−22−22i2i−2i−2i2i2i−2i−2i2−2002−22−20000i2i2−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
χ282222-2-2-2-2-2002-200222−2−22−22i2i−2i−2i2i2i−2i−2i2−2002−22−20000i2i2−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
χ292222-2-2-2-2-2002-200222−2−22−2−2i−2i2i2i−2i−2i2i2i2−2002−22−20000−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
χ302222-2-2-2-2-2002-200222−2−22−2−2i−2i2i2i−2i−2i2i2i2−2002−22−20000−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
χ312222-2-2-2-2-2002-2002−2−222−222i2i−2i−2i2i2i−2i−2i−2200−22−220000−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
χ322222-2-2-2-2-2002-2002−2−222−222i2i−2i−2i2i2i−2i−2i−2200−22−220000−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
χ332222-2-2-2-2-2002-2002−2−222−22−2i−2i2i2i−2i−2i2i2i−2200−22−220000i2i2−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
χ342222-2-2-2-2-2002-2002−2−222−22−2i−2i2i2i−2i−2i2i2i−2200−22−220000i2i2−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
χ3522-2-2-22-2202-2002-202-22-2222−22−22−22−2-2-20000002−22−22−22−22−22−2002i−2i002i−2ii2−i2i2−i2i2−i2i2−i200000000000000000000
χ3622-2-2-22-2202-2002-202-22-2222−22−22−22−2-2-20000002−22−22−22−22−22−200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i200000000000000000000
χ3722-2-2-22-2202-2002-202-22-222−22−22−22−22-2-2000000−22−22−22−22−22−22002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200000000000000000000
χ3822-2-2-22-2202-2002-202-22-222−22−22−22−22-2-2000000−22−22−22−22−22−2200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200000000000000000000
χ3922-2-2-22-2202-2002-20-22-22-2-22−22−22−22−2220000002−22−2−22−22−22−222-2002-2002−2−222−2−2200000000000000000000
χ4022-2-2-22-2202-2002-20-22-22-2-22−22−22−22−2220000002−22−2−22−22−22−22-2200-2200−222−2−222−200000000000000000000
χ4122-2-2-22-2202-2002-20-22-22-2-2−22−22−22−2222000000−22−222−22−22−22−22-2002-200−222−2−222−200000000000000000000
χ4222-2-2-22-2202-2002-20-22-22-2-2−22−22−22−2222000000−22−222−22−22−22−2-2200-22002−2−222−2−2200000000000000000000
χ432-22-2-2-2220-22002-202-22-2-2-22−22−2−22−22220000002−2−222−22−2−22−22002-200-222−22−2−22−2200000000000000000000
χ442-22-2-2-2220-22002-202-22-2-2-22−22−2−22−22220000002−2−222−22−2−22−2200-22002-2−22−222−22−200000000000000000000
χ452-22-2-2-2220-22002-202-22-2-2-2−22−222−22−222000000−222−2−22−222−22−2002-200-22−22−222−22−200000000000000000000
χ462-22-2-2-2220-22002-202-22-2-2-2−22−222−22−222000000−222−2−22−222−22−200-22002-22−22−2−22−2200000000000000000000
χ472-22-2-2-2220-22002-20-22-22222−22−2−22−22-2-20000002−2−22−22−222−22−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i200000000000000000000
χ482-22-2-2-2220-22002-20-22-22222−22−2−22−22-2-20000002−2−22−22−222−22−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i200000000000000000000
χ492-22-2-2-2220-22002-20-22-2222−22−222−22−2-2-2000000−222−22−22−2−22−222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i200000000000000000000
χ502-22-2-2-2220-22002-20-22-2222−22−222−22−2-2-2000000−222−22−22−2−22−22−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i200000000000000000000
χ512-2-222-2-222-2-2-2-22222222-2-200000000-2-22-2-2-2220000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ522-2-222-2-222-2-2-2-22222222-2-200000000-2-22-2-2-222000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ532-2-222-2-222-2-2-2-2222-2-2-2-22200000000222-222-2-20000000000000000000022-2-2-2-22200000000000000000000
χ542-2-222-2-222-2-2-2-2222-2-2-2-22200000000222-222-2-200000000000000000000-2-22222-2-200000000000000000000
χ552-2-222-2-22-22222-2-2-20000002222-2-2-2-2002-20000-2-222000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ562-2-222-2-22-22222-2-2-20000002222-2-2-2-2002-20000-2-222000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ572-2-222-2-22-22222-2-2-2000000-2-2-2-22222002-2000022-2-2000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000
χ582-2-222-2-22-22222-2-2-2000000-2-2-2-22222002-2000022-2-2000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000
χ592-2-222-2-22-2-2-22222-2-2-2-2-2222222-2-2-2-222-22-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000
χ602-2-222-2-22-2-2-22222-2-2-2-2-222-2-2-2-2222222-22-2-222-2-2222222-2-2-2-2000000000000000000000000000000000000
χ612-2-22-222-22002-200-222−2−2−222i2i−2i−2i−2i−2i2i2i−22002−2−220000i2i2−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
χ622-2-22-222-22002-200-222−2−2−222i2i−2i−2i−2i−2i2i2i−22002−2−220000i2i2−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
χ632-2-22-222-22002-200-222−2−2−22−2i−2i2i2i2i2i−2i−2i−22002−2−220000−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
χ642-2-22-222-22002-200-222−2−2−22−2i−2i2i2i2i2i−2i−2i−22002−2−220000−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
χ652-2-22-222-22002-200-2−2−2222−22i2i−2i−2i−2i−2i2i2i2−200−222−20000−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
χ662-2-22-222-22002-200-2−2−2222−22i2i−2i−2i−2i−2i2i2i2−200−222−20000−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
χ672-2-22-222-22002-200-2−2−2222−2−2i−2i2i2i2i2i−2i−2i2−200−222−20000i2i2−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
χ682-2-22-222-22002-200-2−2−2222−2−2i−2i2i2i2i2i−2i−2i2−200−222−20000i2i2−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
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ704444-4-4-4-4400-4400-42222−22−2222−220000000022−2200−2222−2222000000000000000000000000000000000000000000000000
χ714444-4-4-4-4400-4400-4−22−222222−222200000000−22220022−2222−22000000000000000000000000000000000000000000000000
χ7244-4-44-44-40000000022−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i2−222200000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ7344-4-44-44-40000000022−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i2−22220000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ7444-4-44-44-400000000−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i222−220000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ7544-4-44-44-400000000−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i222−2200000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ7644-4-4-44-440-4400-44000000022−2222−2222−2222−2200000000−2222−222200000000000000000000000000000000000000000000
χ7744-4-4-44-440-4400-440000000−2222−2222−2222−22220000000022−2222−2200000000000000000000000000000000000000000000
χ784-44-444-4-40000000022−22−2222−22222i2−2i2−2i22i2−2i22i22i2−2i222−2200000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ794-44-444-4-40000000022−22−2222−2222−2i22i22i2−2i22i2−2i2−2i22i222−220000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ804-44-444-4-400000000−222222−2222−222i2−2i2−2i22i2−2i22i22i2−2i2−22220000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ814-44-444-4-400000000−222222−2222−22−2i22i22i2−2i22i2−2i2−2i22i2−222200000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ824-44-4-4-44404-400-44000000022−2222−22−2222−222200000000−222222−2200000000000000000000000000000000000000000000
χ834-44-4-4-44404-400-440000000−2222−222222−2222−220000000022−22−222200000000000000000000000000000000000000000000
χ844-4-444-4-44444-4-4-4-440000000000000000-440000000000000000000000000000000000000000000000000000
χ854-4-44-444-4-400-440042222−22−22−222200000000−222200−222222−22000000000000000000000000000000000000000000000000
χ864-4-44-444-4-400-44004−22−22222222−220000000022−220022−22−2222000000000000000000000000000000000000000000000000

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