Finite Group Databasebeta

← Group #296754

Character table — Group #296754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444444444444422224444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1111-1
χ172222222222-2-2-222-222-2-222-2-20000-2-222220000000000000000000000-2-20000000000
χ182222222222-2-2-222-222-2-222-2-20000-2-2-2-2-2-20000000000000000000000220000000000
χ192222222222-2-2-222-2-2-222-2-2220000-2-222-2-20000000000000000000000-220000000000
χ202222222222-2-2-222-2-2-222-2-2220000-2-2-2-22200000000000000000000002-20000000000
χ2122222222-2-2222-2-222222-2-2-2-22222-2-20000-2-222-2-20000000000000000000000000000
χ2222222222-2-2222-2-222222-2-2-2-2-2-2-2-2-2-2000022-2-2220000000000000000000000000000
χ2322222222-2-2222-2-22-2-2-2-222222222-2-20000-2-2-2-2220000000000000000000000000000
χ2422222222-2-2222-2-22-2-2-2-22222-2-2-2-2-2-200002222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-22200002200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-2220000220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-200002200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-20000220000000000000000000000000000-222-2000000
χ2922-22-2-22-2002-2-20022-22-200002i2i−2i−2i000000002i−2i00i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ3022-22-2-22-2002-2-20022-22-200002i2i−2i−2i000000002i−2i00−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ3122-22-2-22-2002-2-20022-22-20000−2i−2i2i2i00000000−2i2i00i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ3222-22-2-22-2002-2-20022-22-20000−2i−2i2i2i00000000−2i2i00−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ3322-22-2-22-2002-2-2002-22-2200002i2i−2i−2i00000000−2i2i00i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ3422-22-2-22-2002-2-2002-22-2200002i2i−2i−2i00000000−2i2i00−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ3522-22-2-22-2002-2-2002-22-220000−2i−2i2i2i000000002i−2i00i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ3622-22-2-22-2002-2-2002-22-220000−2i−2i2i2i000000002i−2i00−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ372-22-22-22-22-2-22-22-22000000002i−2i2i−2i2-200002i−2i000000002i−2i2i−2i00002-22-2000000000000
χ382-22-22-22-22-2-22-22-22000000002i−2i2i−2i2-200002i−2i00000000−2i2i−2i2i0000-22-22000000000000
χ392-22-22-22-22-2-22-22-2200000000−2i2i−2i2i2-20000−2i2i000000002i−2i2i−2i0000-22-22000000000000
χ402-22-22-22-22-2-22-22-2200000000−2i2i−2i2i2-20000−2i2i00000000−2i2i−2i2i00002-22-2000000000000
χ412-22-22-22-2-22-22-2-222000000002i−2i2i−2i-220000−2i2i00002i−2i2i−2i00002-22-20000000000000000
χ422-22-22-22-2-22-22-2-222000000002i−2i2i−2i-220000−2i2i0000−2i2i−2i2i0000-22-220000000000000000
χ432-22-22-22-2-22-22-2-22200000000−2i2i−2i2i-2200002i−2i00002i−2i2i−2i0000-22-220000000000000000
χ442-22-22-22-2-22-22-2-22200000000−2i2i−2i2i-2200002i−2i0000−2i2i−2i2i00002-22-20000000000000000
χ452-2-2-2-222200-2-2200200002-22-22-2-2200000000002-22−2−222−2−222−2−222−2−22000000000000
χ462-2-2-2-222200-2-2200200002-22-22-2-2200000000002-2−222−2−222−2−222−2−222−2000000000000
χ472-2-2-2-222200-2-2200200002-22-2-222-20000000000-222−2−222−2−22−222−2−222−2000000000000
χ482-2-2-2-222200-2-2200200002-22-2-222-20000000000-22−222−2−222−22−2−222−2−22000000000000
χ492-2-2-2-222200-2-220020000-22-222-2-220000000000-222−2−22−222−22−2−22−222−2000000000000
χ502-2-2-2-222200-2-220020000-22-222-2-220000000000-22−222−22−2−22−222−22−2−22000000000000
χ512-2-2-2-222200-2-220020000-22-22-222-200000000002-22−2−22−222−2−222−22−2−22000000000000
χ522-2-2-2-222200-2-220020000-22-22-222-200000000002-2−222−22−2−222−2−22−222−2000000000000
χ53444-4-44-4-44-4000-44000000000000000004-40000000000000000000000000000000000
χ54444-4-44-4-44-4000-4400000000000000000-440000000000000000000000000000000000
χ55444-4-44-4-4-440004-40000000000000004-4000000000000000000000000000000000000
χ56444-4-44-4-4-440004-4000000000000000-44000000000000000000000000000000000000
χ5744-44-4-44-400-44400-44-4-44000000000000000000000000000000000000000000000000
χ5844-44-4-44-400-44400-4-444-4000000000000000000000000000000000000000000000000
χ594-444-4-4-4444000-4-4000000000000000000000000000000000000000000000002i2−2i20000
χ604-444-4-4-4444000-4-400000000000000000000000000000000000000000000000−2i22i20000
χ614-444-4-4-44-4-400044000000000000000000000000000000000000000000000000022−2200
χ624-444-4-4-44-4-4000440000000000000000000000000000000000000000000000000−222200
χ634-44-44-44-44-44-444-4-4000000000000-4400000000000000000000000000000000000000
χ644-44-44-44-4-444-44-44-40000000000004-400000000000000000000000000000000000000
χ654-4-4-4-44440044-400-400004-4-4400000000000000000000000000000000000000000000
χ664-4-4-4-44440044-400-40000-444-400000000000000000000000000000000000000000000
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8888-8-8000000000000000000000000000000000000000000000000000000000000

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