Finite Group Databasebeta

← Group #257041

Character table — Group #257041

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444444444888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-11-1-111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111111111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-11-11-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-11-111111-1-1-1-1
χ91111111111-1-1-1-111-1-11-1-111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-11-11-1111-1-111-1-1
χ101111111111-1-1-1-111-1-11-1-111111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-11-11-11-1-111-1-111
χ111111111111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1111-11-111-1-1-1-111
χ121111111111-1-1-1-111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1111-11-1-1-11111-1-1
χ131111111111-1-1-1-111-1-11-1-1111-1-1-11111111111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-111-1-111
χ141111111111-1-1-1-111-1-11-1-1111-1-1-1111111-1-1-1-11111-1-1-1-11111111-1-1-1-1-111-1-111-1-1
χ151111111111-1-1-1-111-1-11-1-1111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-11111-1-1
χ161111111111-1-1-1-111-1-11-1-1111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1111111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-222-222000000000000000000000-20-2000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2000000000000000000000202000000000000
χ192222222222-2-2-2-222-2-2-222-2-2-2222-2-200000000000000000000020-2000000000000
χ202222222222-2-2-2-222-2-2-222-2-2-2-2-2222000000000000000000000-202000000000000
χ2122222222-2-22222-2-2-2-2222-2-2200-20022-2-20000000000000000000020-2000000000
χ2222222222-2-22222-2-2-2-2222-2-2200-200-2-22200000000000000000000-202000000000
χ2322222222-2-22222-2-2-2-2-2-2-222-2002000000000000000000000020-200-20200000000
χ2422222222-2-22222-2-2-2-2-2-2-222-20020000000000000000000000-2020020-200000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-2-220020022-2-200000000000000000000-202000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-2-2200200-2-2220000000000000000000020-2000000000
χ2722222222-2-2-2-2-2-2-2-222-22222-200-2000000000000000000000020-20020-200000000
χ2822222222-2-2-2-2-2-2-2-222-22222-200-20000000000000000000000-20200-20200000000
χ2922-2-222-2-22-200002-200-2002-22000002i−2i2i−2i00002i2i−2i−2i000022-2-20000000000000000
χ3022-2-222-2-22-200002-200-2002-22000002i−2i2i−2i0000−2i−2i2i2i0000-2-2220000000000000000
χ3122-2-222-2-22-200002-200-2002-2200000−2i2i−2i2i00002i2i−2i−2i0000-2-2220000000000000000
χ3222-2-222-2-22-200002-200-2002-2200000−2i2i−2i2i0000−2i−2i2i2i000022-2-20000000000000000
χ3322-2-222-2-2-220000-2200-200-222000002i−2i−2i2i2i2i−2i−2i000022-2-200000000000000000000
χ3422-2-222-2-2-220000-2200-200-222000002i−2i−2i2i−2i−2i2i2i0000-2-22200000000000000000000
χ3522-2-222-2-2-220000-2200-200-22200000−2i2i2i−2i2i2i−2i−2i0000-2-22200000000000000000000
χ3622-2-222-2-2-220000-2200-200-22200000−2i2i2i−2i−2i−2i2i2i000022-2-200000000000000000000
χ372-2-2-22-222-2-222-2-2222-20000002-202-20000000000002−22−22−22−20000000000002−22−2
χ382-2-2-22-222-2-222-2-2222-20000002-202-2000000000000−22−22−22−22000000000000−22−22
χ392-2-2-22-222-2-222-2-2222-2000000-220-220000000000002−22−22−22−2000000000000−22−22
χ402-2-2-22-222-2-222-2-2222-2000000-220-22000000000000−22−22−22−220000000000002−22−2
χ412-2-2-22-222-2-2-2-22222-220000002-20-220000000000002−22−2−22−220000000000002−2−22
χ422-2-2-22-222-2-2-2-22222-220000002-20-22000000000000−22−222−22−2000000000000−222−2
χ432-2-2-22-222-2-2-2-22222-22000000-2202-20000000000002−22−2−22−22000000000000−222−2
χ442-2-2-22-222-2-2-2-22222-22000000-2202-2000000000000−22−222−22−20000000000002−2−22
χ45444-4-4-4-44004-44-400000000000000000000000000000000000000000002i−2i2i−2i0000
χ46444-4-4-4-44004-44-40000000000000000000000000000000000000000000−2i2i−2i2i0000
χ47444-4-4-4-4400-44-4400000000000000000000000000000000000000000002i−2i−2i2i0000
χ48444-4-4-4-4400-44-440000000000000000000000000000000000000000000−2i2i2i−2i0000
χ4944-4-444-4-44-400004-400400-44-400000000000000000000000000000000000000000
χ5044-4-444-4-4-440000-44004004-4-400000000000000000000000000000000000000000
χ514-4444-4-4-44-40000-44000000000000000000000000022−22−222200000000000000000000
χ524-4444-4-4-44-40000-440000000000000000000000000−222222−2200000000000000000000
χ534-4444-4-4-4-4400004-40000000000000000000000000000022−22−22220000000000000000
χ544-4444-4-4-4-4400004-400000000000000000000000000000−222222−220000000000000000
χ554-44-4-444-4000000000004-40000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ564-44-4-444-4000000000004-4000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ574-44-4-444-400000000000-440000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ584-44-4-444-400000000000-44000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ594-4-44-44-44004-4-4400000000000000000002-2-222-2-22000000000000000000000000
χ604-4-44-44-44004-4-440000000000000000000-222-2-222-2000000000000000000000000
χ614-4-44-44-4400-444-400000000000000000002-2-22-222-2000000000000000000000000
χ624-4-44-44-4400-444-40000000000000000000-222-22-2-22000000000000000000000000
χ634-4-4-44-4444444-4-4-4-4-4400000000000000000000000000000000000000000000000
χ644-4-4-44-44444-4-444-4-44-400000000000000000000000000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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