Finite Group Databasebeta

← Group #501913

Character table — Group #501913

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488881616161616161616161616161616161622444488881616161616161616224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1111111-1-11111-1-1-1-111-1-111-1-1-1-11-1
χ101111111111-1-1-1-11111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-11
χ111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1-11
χ121111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1
χ131111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1111111-1-1-1-111-1-1-11
χ141111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1111-1
χ151111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-1111111-1-1-1-1-1-111-1-111-1-11-1
χ161111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-11
χ172222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000220000-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-20000000000000000-2-20000222200000000000000000000
χ192222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000002-20000-2-22200000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-22000022-2-200000000000000000000
χ2122222222-2-22222-2-200000000-2-2222200002222−2−2−2−22222−2−2−2−2-2-20000000022−2−222−2−2000000000000
χ2222222222-2-22222-2-200000000-2-222220000−2−2−2−22222−2−2−2−22222-2-200000000−2−222−2−222000000000000
χ2322222222-2-22222-2-200000000-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−22200000000−2−222−2−222000000000000
χ2422222222-2-22222-2-200000000-2-2-2-2-2-20000−2−2−2−22222−2−2−2−22222220000000022−2−222−2−2000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-200002222−2−2−2−2−2−2−2−22222-220000000022−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-20000−2−2−2−222222222−2−2−2−2-2200000000−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-22200002222−2−2−2−2−2−2−2−222222-200000000−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-2220000−2−2−2−222222222−2−2−2−22-20000000022−2−2−2−222000000000000
χ2922-22-2-2-222-20000-222222-2-2-2-200000000002i2i−2i−2i2i2i−2i−2i00000000002i2i−2i−2i0000000000002-20000000000
χ3022-22-2-2-222-20000-222222-2-2-2-200000000002i2i−2i−2i2i2i−2i−2i0000000000−2i−2i2i2i000000000000-220000000000
χ3122-22-2-2-222-20000-222222-2-2-2-20000000000−2i−2i2i2i−2i−2i2i2i00000000002i2i−2i−2i000000000000-220000000000
χ3222-22-2-2-222-20000-222222-2-2-2-20000000000−2i−2i2i2i−2i−2i2i2i0000000000−2i−2i2i2i0000000000002-20000000000
χ3322-2-2-222-20022-2-2002−22−22−22−2002i−2i2i−2i22−2−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000i2−i2i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3422-2-2-222-20022-2-2002−22−22−22−2002i−2i2i−2i22−2−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000i2−i2i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3522-2-2-222-20022-2-2002−22−22−22−200−2i2i−2i2i22−2−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−i2i2−i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ3622-2-2-222-20022-2-2002−22−22−22−200−2i2i−2i2i22−2−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−i2i2−i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ3722-2-2-222-20022-2-200−22−22−22−22002i−2i2i−2i−2−222ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−i2i2−i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3822-2-2-222-20022-2-200−22−22−22−22002i−2i2i−2i−2−222−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−i2i2−i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3922-2-2-222-20022-2-200−22−22−22−2200−2i2i−2i2i−2−222ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000i2−i2i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4022-2-2-222-20022-2-200−22−22−22−2200−2i2i−2i2i−2−222−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000i2−i2i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4122-2-2-222-200-2-222002−22−22−22−2002i−2i−2i2i−2−222ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000i2−i2−i2i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4222-2-2-222-200-2-222002−22−22−22−2002i−2i−2i2i−2−222−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000i2−i2−i2i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4322-2-2-222-200-2-222002−22−22−22−200−2i2i2i−2i−2−222ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−i2i2i2−i2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4422-2-2-222-200-2-222002−22−22−22−200−2i2i2i−2i−2−222−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−i2i2i2−i2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4522-2-2-222-200-2-22200−22−22−22−22002i−2i−2i2i22−2−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−i2i2i2−i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4622-2-2-222-200-2-22200−22−22−22−22002i−2i−2i2i22−2−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−i2i2i2−i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4722-2-2-222-200-2-22200−22−22−22−2200−2i2i2i−2i22−2−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000i2−i2−i2i2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4822-2-2-222-200-2-22200−22−22−22−2200−2i2i2i−2i22−2−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000i2−i2−i2i2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ492-222-22-2-2-2-22-22-22222-2-2-2-2222-200002-22-20000000000000000002i−2i2i−2i000000000000000000002i−2i00
χ502-222-22-2-2-2-22-22-22222-2-2-2-2222-200002-22-2000000000000000000−2i2i−2i2i00000000000000000000−2i2i00
χ512-222-22-2-2-2-22-22-222-2-22222-2-22-20000-22-22000000000000000000000000000000000000002i−2i2i−2i0000
χ522-222-22-2-2-2-22-22-222-2-22222-2-22-20000-22-2200000000000000000000000000000000000000−2i2i−2i2i0000
χ532-222-22-2-2-2-2-22-222222-2-2-2-222-220000-22-220000000000000000002i−2i2i−2i00000000000000000000−2i2i00
χ542-222-22-2-2-2-2-22-222222-2-2-2-222-220000-22-22000000000000000000−2i2i−2i2i000000000000000000002i−2i00
χ552-222-22-2-2-2-2-22-2222-2-22222-2-2-2200002-22-2000000000000000000000000000000000000002i−2i−2i2i0000
χ562-222-22-2-2-2-2-22-2222-2-22222-2-2-2200002-22-200000000000000000000000000000000000000−2i2i2i−2i0000
χ572-2-222-22-2-220000-2222-2-222-2-20000000000000000002i−2i2i−2i2i−2i2i−2i002-2-22000000000000002i−2i00000000
χ582-2-222-22-2-220000-2222-2-222-2-20000000000000000002i−2i2i−2i2i−2i2i−2i00-222-200000000000000−2i2i00000000
χ592-2-222-22-2-220000-2222-2-222-2-2000000000000000000−2i2i−2i2i−2i2i−2i2i002-2-2200000000000000−2i2i00000000
χ602-2-222-22-2-220000-2222-2-222-2-2000000000000000000−2i2i−2i2i−2i2i−2i2i00-222-2000000000000002i−2i00000000
χ61444-44-4-4-40000000022−2222−22−2222−222200000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000000000
χ62444-44-4-4-40000000022−2222−22−2222−22220000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000000000
χ63444-44-4-4-400000000−2222−222222−2222−2200000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000000000
χ64444-44-4-4-400000000−2222−222222−2222−220000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000000000
χ6544-44-4-4-444-40000-44-4-4-4-4444400000000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44-4400004-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ6744-44-4-4-44-4400004-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ684-444-44-4-4444-44-4-4-400000000-44000000000000000000000000000000000000000000000000000000
χ694-444-44-4-444-44-44-4-4000000004-4000000000000000000000000000000000000000000000000000000
χ704-44-4-4-4440000000022−22−222222−22−22220000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ714-44-4-4-4440000000022−22−222222−22−2222000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ724-44-4-4-44400000000−222222−22−222222−220000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ734-44-4-4-44400000000−222222−22−222222−22000000000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ744-4-444-44-44-400004-4000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ754-4-444-44-44-400004-400000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ764-4-444-44-4-440000-44-4-444-4-44400000000000000000000000000000000000000000000000000000000
χ774-4-4-444-44004-4-440022−22−2222−222222−2200000022−22−22220000000000000000000000000000000000000000000000
χ784-4-4-444-44004-4-4400−222222−2222−22−2222000000−222222−220000000000000000000000000000000000000000000000
χ794-4-4-444-4400-444-40022−22−2222−222222−22000000−222222−220000000000000000000000000000000000000000000000
χ804-4-4-444-4400-444-400−222222−2222−22−222200000022−22−22220000000000000000000000000000000000000000000000

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