Finite Group Databasebeta

← Group #241967

Character table — Group #241967

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444444444448888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ121111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ131111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ141111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ151111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ161111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1722222222222222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2000000-2-2000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-22200000022000000000000000000000000000000
χ192222222222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2-2-200000022000000000000000000000000000000
χ202222222222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22222000000-2-2000000000000000000000000000000
χ2122222222-2-22222222222-2-222-2-2-2-2-2-200000022-2-2-2-200220000000000000000000000000000
χ2222222222-2-22222222222-2-222-2-2-2-2-2-2000000-2-2222200-2-20000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000002-22-2000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000-22-22000000
χ2522222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-200000022-2-22200-2-20000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2000000-2-222-2-200220000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000-222-2000000
χ2922-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i002-20000000000002-20000002i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i2000000000000
χ3022-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i002-20000000000002-20000002i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i2000000000000
χ3122-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i002-2000000000000-22000000−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ3222-2-222-2-2002i2i−2i−2i2-22i2i−2i−2i002-2000000000000-22000000−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ3322-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i002-20000000000002-2000000−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i2000000000000
χ3422-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i002-20000000000002-2000000−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i2000000000000
χ3522-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i002-2000000000000-220000002i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ3622-2-222-2-200−2i−2i2i2i2-2−2i−2i2i2i002-2000000000000-220000002i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ372-22-22-22-22-22i−2i2i−2i2-22i−2i2i−2i2-2-222i−2i2i−2i2-20000000000000000000000002i−2i2i−2i2-22-2000000000000
χ382-22-22-22-22-22i−2i2i−2i2-22i−2i2i−2i2-2-222i−2i2i−2i2-2000000000000000000000000−2i2i−2i2i-22-22000000000000
χ392-22-22-22-22-22i−2i2i−2i-22−2i2i−2i2i2-22-22i−2i−2i2i-2200000000000000000000000000000000000000002-22i−2i
χ402-22-22-22-22-22i−2i2i−2i-22−2i2i−2i2i2-22-22i−2i−2i2i-220000000000000000000000000000000000000000-22−2i2i
χ412-22-22-22-22-2−2i2i−2i2i2-2−2i2i−2i2i2-2-22−2i2i−2i2i2-20000000000000000000000002i−2i2i−2i-22-22000000000000
χ422-22-22-22-22-2−2i2i−2i2i2-2−2i2i−2i2i2-2-22−2i2i−2i2i2-2000000000000000000000000−2i2i−2i2i2-22-2000000000000
χ432-22-22-22-22-2−2i2i−2i2i-222i−2i2i−2i2-22-2−2i2i2i−2i-2200000000000000000000000000000000000000002-2−2i2i
χ442-22-22-22-22-2−2i2i−2i2i-222i−2i2i−2i2-22-2−2i2i2i−2i-220000000000000000000000000000000000000000-222i−2i
χ452-22-22-22-2-222i−2i2i−2i2-22i−2i2i−2i-22-22−2i2i−2i2i-2200000000000000002-22-22i−2i2i−2i00000000000000000000
χ462-22-22-22-2-222i−2i2i−2i2-22i−2i2i−2i-22-22−2i2i−2i2i-220000000000000000-22-22−2i2i−2i2i00000000000000000000
χ472-22-22-22-2-222i−2i2i−2i-22−2i2i−2i2i-222-2−2i2i2i−2i2-2000000000000000000000000000000002-200002i−2i0000
χ482-22-22-22-2-222i−2i2i−2i-22−2i2i−2i2i-222-2−2i2i2i−2i2-200000000000000000000000000000000-220000−2i2i0000
χ492-22-22-22-2-22−2i2i−2i2i2-2−2i2i−2i2i-22-222i−2i2i−2i-2200000000000000002-22-2−2i2i−2i2i00000000000000000000
χ502-22-22-22-2-22−2i2i−2i2i2-2−2i2i−2i2i-22-222i−2i2i−2i-220000000000000000-22-222i−2i2i−2i00000000000000000000
χ512-22-22-22-2-22−2i2i−2i2i-222i−2i2i−2i-222-22i−2i−2i2i2-2000000000000000000000000000000002-20000−2i2i0000
χ522-22-22-22-2-22−2i2i−2i2i-222i−2i2i−2i-222-22i−2i−2i2i2-200000000000000000000000000000000-2200002i−2i0000
χ532-2-222-2-22002-2-22222-2-2200-2-2000000000000002i−2i2i−2i00002−2−222−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ542-2-222-2-22002-2-22222-2-2200-2-2000000000000002i−2i2i−2i0000−222−2−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ552-2-222-2-22002-2-22222-2-2200-2-200000000000000−2i2i−2i2i00002−2−222−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ562-2-222-2-22002-2-22222-2-2200-2-200000000000000−2i2i−2i2i0000−222−2−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ572-2-222-2-2200-222-222-222-200-2-2000000000000002i−2i−2i2i00002−2−22−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ582-2-222-2-2200-222-222-222-200-2-2000000000000002i−2i−2i2i0000−222−22−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ592-2-222-2-2200-222-222-222-200-2-200000000000000−2i2i2i−2i00002−2−22−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ602-2-222-2-2200-222-222-222-200-2-200000000000000−2i2i2i−2i0000−222−22−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ614444-4-4-4-44-40000000000-44000000004-4000000000000000000000000000000000000000000
χ624444-4-4-4-44-40000000000-4400000000-44000000000000000000000000000000000000000000
χ634444-4-4-4-4-4400000000004-400000000004-40000000000000000000000000000000000000000
χ644444-4-4-4-4-4400000000004-40000000000-440000000000000000000000000000000000000000
χ6544-4-444-4-4004i4i−4i−4i-44−4i−4i4i4i00-4400000000000000000000000000000000000000000000000000
χ6644-4-444-4-400−4i−4i4i4i-444i4i−4i−4i00-4400000000000000000000000000000000000000000000000000
χ674-44-4-44-44440000000000-4-40000000000004i−4i00000000000000000000000000000000000000
χ684-44-4-44-44440000000000-4-4000000000000−4i4i00000000000000000000000000000000000000
χ694-44-4-44-44-4-4000000000044000000000000000000004-4000000000000000000000000000000
χ704-44-4-44-44-4-400000000004400000000000000000000-44000000000000000000000000000000
χ714-4-444-4-44004-4-44-4-4-444-4004400000000000000000000000000000000000000000000000000
χ724-4-444-4-4400-444-4-4-44-4-44004400000000000000000000000000000000000000000000000000
χ7388-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).