Finite Group Databasebeta

← Group #267705

Character table — Group #267705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-11-1-1-1-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1111-11-1-1-1-1
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-11-11111
χ91111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-111-1-1
χ101111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1111-1-111
χ111111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1-111111-1-1
χ121111111111-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-111-1-1-1-1-111
χ131111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11-11-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1111-11-111-1-1
χ151111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1111-11-1-1-111
χ161111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-11-1111-1-1
χ172222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22222-2-200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-200002-222-2-22-2000000000000000000000000002-22000-200000
χ2222222222-2-22222-2-2-2-200002-222-2-22-200000000000000000000000000-22-2000200000
χ2322222222-2-22222-2-2-2-20000-22-2-222-22000000000000000000000000000002-220-20000
χ2422222222-2-22222-2-2-2-20000-22-2-222-2200000000000000000000000000000-22-2020000
χ2522222222-2-2-2-2-2-2-2-22200002-2-2-2222-2000000000000000000000000002-2-2000200000
χ2622222222-2-2-2-2-2-2-2-22200002-2-2-2222-200000000000000000000000000-222000-200000
χ2722222222-2-2-2-2-2-2-2-2220000-2222-2-2-22000000000000000000000000000002-2-2020000
χ2822222222-2-2-2-2-2-2-2-2220000-2222-2-2-2200000000000000000000000000000-2220-20000
χ292222-2-2-2-2-2-222-2-2222-222-2-2000000002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ302222-2-2-2-2-2-222-2-2222-222-2-2000000002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ312222-2-2-2-2-2-222-2-2222-2-2-22200000000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ322222-2-2-2-2-2-222-2-2222-2-2-22200000000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ332222-2-2-2-2-2-2-2-22222-2222-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ342222-2-2-2-2-2-2-2-22222-2222-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352222-2-2-2-2-2-2-2-22222-22-2-222000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ362222-2-2-2-2-2-2-2-22222-22-2-222000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-22-222-2-22-200002-2002-22-2002i−2i2i−2i0000002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ382-22-222-2-22-200002-2002-22-2002i−2i2i−2i0000002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ392-22-222-2-22-200002-2002-22-200−2i2i−2i2i000000−2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ402-22-222-2-22-200002-2002-22-200−2i2i−2i2i000000−2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ412-22-222-2-22-200002-200-22-22002i−2i2i−2i000000−2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000000000
χ422-22-222-2-22-200002-200-22-22002i−2i2i−2i000000−2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000000000
χ432-22-222-2-22-200002-200-22-2200−2i2i−2i2i0000002i−2i2−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ442-22-222-2-22-200002-200-22-2200−2i2i−2i2i0000002i−2i−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ452-22-2-2-222-2200002-2002-2-22220000-2-2002-2002i−2i−2i2i00002i−2i−2i2i00000000000000000000
χ462-22-2-2-222-2200002-2002-2-22220000-2-2002-200−2i2i2i−2i0000−2i2i2i−2i00000000000000000000
χ472-22-2-2-222-2200002-2002-2-22-2-200002200-220000002-2-2200002-2-220000000000000000
χ482-22-2-2-222-2200002-2002-2-22-2-200002200-22000000-222-20000-222-20000000000000000
χ492-22-2-2-222-2200002-200-222-2220000-2-200-22002i−2i−2i2i0000−2i2i2i−2i00000000000000000000
χ502-22-2-2-222-2200002-200-222-2220000-2-200-2200−2i2i2i−2i00002i−2i−2i2i00000000000000000000
χ512-22-2-2-222-2200002-200-222-2-2-2000022002-20000002-2-220000-222-20000000000000000
χ522-22-2-2-222-2200002-200-222-2-2-2000022002-2000000-222-200002-2-220000000000000000
χ534444-4-4-4-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ554-44-444-4-4-440000-44000000004i−4i−4i4i0000000000000000000000000000000000000000
χ564-44-444-4-4-440000-4400000000−4i4i4i−4i0000000000000000000000000000000000000000
χ574-44-4-4-4444-40000-440000004-40000-4400000000000000000000000000000000000000
χ584-44-4-4-4444-40000-44000000-4400004-400000000000000000000000000000000000000
χ594-4-444-44-4004-44-4000000000000000000000000000000000000000000000000002i−2i2i−2i
χ604-4-444-44-4004-44-400000000000000000000000000000000000000000000000000−2i2i−2i2i
χ614-4-444-44-400-44-44000000000000000000000000000000000000000000000000002i−2i−2i2i
χ624-4-444-44-400-44-4400000000000000000000000000000000000000000000000000−2i2i2i−2i
χ634-4-44-44-44004-4-44000000000000000000000000000000000000002-22-2000000000000
χ644-4-44-44-44004-4-4400000000000000000000000000000000000000-22-22000000000000
χ654-4-44-44-4400-444-4000000000000000000000000000000000000002-2-22000000000000
χ664-4-44-44-4400-444-400000000000000000000000000000000000000-222-2000000000000
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ6888-8-8-888-8000000000000000000000000000000000000000000000000000000000000

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