Finite Group Databasebeta

← Group #271080

Character table — Group #271080

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444422444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ611111111111111111111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1
χ711111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1111111-1-1
χ811111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1-1-111
χ91111111111111111-1-11-1-1-1-11111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-111-1-11-1
χ101111111111111111-1-11-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-11
χ111111111111111111-1-11-1-1-1-11111-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-1-111-11
χ121111111111111111-1-11-1-1-1-11111-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-11-1
χ131111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-111-1-1111-1
χ141111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-11111-1-1-11
χ151111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-11
χ161111111111111111-1-11-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1111-1
χ172222222222-2-2-222-222-2-2-2222222-2-2-22200-2-200-2-20000000000000000000000000000
χ182222222222-2-2-222-222-2-2-222-2-2-2-2-2-2-2-2-2002200220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-222-2-2222222-2-2-200-2-200220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-222-2-2-2-2-2-222-222002200-2-20000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-2-2-2000022-2002200-2-2000000000000000000-200200000000
χ2222222222-2-2222-2-2222-2-2-2-2-2000022-200-2-20022000000000000000000200-200000000
χ2322222222-2-2222-2-22-2-2-222220000-2-2-200220022000000000000000000-200-200000000
χ2422222222-2-2222-2-22-2-2-222220000-2-2-200-2-200-2-2000000000000000000200200000000
χ2522222222-2-2-2-2-2-2-2-222222-2-20000-2-220000000000000000000000000002-202-2000000
χ2622222222-2-2-2-2-2-2-2-222222-2-20000-2-22000000000000000000000000000-220-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22-2-22200002220000000000000000000000000002-20-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22-2-2220000222000000000000000000000000000-2202-2000000
χ2922-22-2-22-2-2-20002202-20002-222-2-20002-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ3022-22-2-22-2-2-20002202-20002-222-2-20002-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ3122-22-2-22-2-2-20002202-20002-2-2-222000-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ3222-22-2-22-2-2-20002202-20002-2-2-222000-2200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ3322-22-2-22-2-2-2000220-22000-2222-2-2000-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ3422-22-2-22-2-2-2000220-22000-2222-2-2000-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3522-22-2-22-2-2-2000220-22000-22-2-2220002-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3622-22-2-22-2-2-2000220-22000-22-2-2220002-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-22-22-22-22-20002-200002i−2i002-22-22i−2i0000000002i−2ii2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-22-22-22-22-20002-200002i−2i002-22-22i−2i0000000002i−2i−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-22-22-22-22-20002-200002i−2i00-22-222i−2i000000000−2i2ii2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ402-22-22-22-22-20002-200002i−2i00-22-222i−2i000000000−2i2i−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ412-22-22-22-22-20002-20000−2i2i002-22-2−2i2i000000000−2i2ii2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ422-22-22-22-22-20002-20000−2i2i002-22-2−2i2i000000000−2i2i−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ432-22-22-22-22-20002-20000−2i2i00-22-22−2i2i0000000002i−2ii2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-22-22-22-22-20002-20000−2i2i00-22-22−2i2i0000000002i−2i−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-2-2-2-2222-2222-22-2-200200002-2-2200-200002-2000000002i−2i−2i2i00002i−2i−2i2i000000000000
χ462-2-2-2-2222-2222-22-2-200200002-2-2200-200002-200000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ472-2-2-2-2222-2222-22-2-20020000-222-200-20000-22000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ482-2-2-2-2222-2222-22-2-20020000-222-200-20000-2200000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ492-2-2-2-2222-22-2-222-2200-200002-2-220020000-2200002-2-2200002-2-220000000000000000
χ502-2-2-2-2222-22-2-222-2200-200002-2-220020000-220000-222-20000-222-20000000000000000
χ512-2-2-2-2222-22-2-222-2200-20000-222-200200002-200002-2-220000-222-20000000000000000
χ522-2-2-2-2222-22-2-222-2200-20000-222-200200002-20000-222-200002-2-220000000000000000
χ53444-4-4-4-44004-4400-400000000000000004-40000000000000000000000000000000000
χ54444-4-4-4-44004-4400-40000000000000000-440000000000000000000000000000000000
χ55444-4-4-4-4400-44-4004000000000000000000004i−4i000000000000000000000000000000
χ56444-4-4-4-4400-44-400400000000000000000000−4i4i000000000000000000000000000000
χ5744-44-4-44-444000-4-404-4000-44000000000000000000000000000000000000000000000
χ5844-44-4-44-444000-4-40-440004-4000000000000000000000000000000000000000000000
χ594-44-44-44-4-44000-4400004i−4i000000−4i4i000000000000000000000000000000000000000
χ604-44-44-44-4-44000-440000−4i4i0000004i−4i000000000000000000000000000000000000000
χ614-4-444-4-44004-4-400400000000000000000000000000000000000000000000000022−2200
χ624-4-444-4-44004-4-4004000000000000000000000000000000000000000000000000−222200
χ634-4-444-4-4400-44400-400000000000000000000000000000000000000000000002i2−2i20000
χ644-4-444-4-4400-44400-40000000000000000000000000000000000000000000000−2i22i20000
χ654-4-4-4-44444-444-4-44-400-40000000000400000000000000000000000000000000000000
χ664-4-4-4-44444-4-4-44-4440040000000000-400000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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