Finite Group Databasebeta

← Group #258665

Character table — Group #258665

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444422444444488888888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-11-1-1111-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-1-1-11-1-1111-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-11-1-1-1-11111-1-111
χ121111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1111-1-111-1-111-1-1
χ131111111111111111-1-1-1-11-1-11-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11-111-1-111-1-1-1-111
χ141111111111111111-1-1-1-11-1-11-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1111111-1-1
χ151111111111111111-1-1-1-11-1-11-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-11-1-11-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11111111-1-1-1-1-1-111
χ1722222222222-2-2-2-222222-2-2-2-222-22200000000000000000000-20-20000000000000
χ1822222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2000000000000000000002020000000000000
χ1922222222222-2-2-2-22-2-2-2-2-222-2222-2-200000000000000000000-2020000000000000
χ2022222222222-2-2-2-22-2-2-2-2-222-2-2-22220000000000000000000020-20000000000000
χ2122222222-2-2-22222-222-2-2-222-200-20022-2-20000000000000000020-2000000000000
χ2222222222-2-2-22222-222-2-2-222-200-200-2-22200000000000000000-202000000000000
χ2322222222-2-2-22222-2-2-222-2-2-2-20020022-2-200000000000000000-202000000000000
χ2422222222-2-2-22222-2-2-222-2-2-2-200200-2-2220000000000000000020-2000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22-2-2200200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22-2-220020000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222200-200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200-20000000000000000000000000000-222-2000000
χ292222-2-2-2-222-20000-22-22-200002-202-2000022−2−222−2−222−2−222−2−20000000000000000
χ302222-2-2-2-222-20000-22-22-200002-202-20000−2−222−2−222−2−222−2−2220000000000000000
χ312222-2-2-2-222-20000-22-22-20000-220-22000022−2−222−2−2−2−222−2−2220000000000000000
χ322222-2-2-2-222-20000-22-22-20000-220-220000−2−222−2−22222−2−222−2−20000000000000000
χ332222-2-2-2-222-20000-2-22-2200002-20-22000022−2−2−2−22222−2−2−2−2220000000000000000
χ342222-2-2-2-222-20000-2-22-2200002-20-220000−2−22222−2−2−2−22222−2−20000000000000000
χ352222-2-2-2-222-20000-2-22-220000-2202-2000022−2−2−2−222−2−22222−2−20000000000000000
χ362222-2-2-2-222-20000-2-22-220000-2202-20000−2−22222−2−222−2−2−2−2220000000000000000
χ372-2-22-222-22-222-22-2-20000-2002000002i−2i2i−2i00002-22-20000000000000000002i−2i0000
χ382-2-22-222-22-222-22-2-20000-2002000002i−2i2i−2i0000-22-22000000000000000000−2i2i0000
χ392-2-22-222-22-222-22-2-20000-200200000−2i2i−2i2i00002-22-2000000000000000000−2i2i0000
χ402-2-22-222-22-222-22-2-20000-200200000−2i2i−2i2i0000-22-220000000000000000002i−2i0000
χ412-2-22-222-2-22-22-22-220000200-2000002i−2i−2i2i2i−2i2i−2i00000000000000002-20000000000
χ422-2-22-222-2-22-22-22-220000200-2000002i−2i−2i2i−2i2i−2i2i0000000000000000-220000000000
χ432-2-22-222-2-22-22-22-220000200-200000−2i2i2i−2i2i−2i2i−2i0000000000000000-220000000000
χ442-2-22-222-2-22-22-22-220000200-200000−2i2i2i−2i−2i2i−2i2i00000000000000002-20000000000
χ454444-4-4-4-4-4-44000044-4-44000000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4400004-444-4000000000000000000000000000000000000000000000
χ4744-4-444-4-40004-4-440000000000000000000000000022−2222−2200000000000000000000
χ4844-4-444-4-40004-4-4400000000000000000000000000−2222−222200000000000000000000
χ4944-4-444-4-4000-444-400000000000000000000000000000022−2222−220000000000000000
χ5044-4-444-4-4000-444-4000000000000000000000000000000−2222−22220000000000000000
χ5144-4-4-4-44400000000000004-40000000000000000002-2-222-2-220000000000000000
χ5244-4-4-4-44400000000000004-4000000000000000000-222-2-222-20000000000000000
χ5344-4-4-4-4440000000000000-440000000000000000002-2-22-222-20000000000000000
χ5444-4-4-4-4440000000000000-44000000000000000000-222-22-2-220000000000000000
χ554-44-4-44-4400044-4-400000000000000000000000000000000000000000000002i2−2i200
χ564-44-4-44-4400044-4-40000000000000000000000000000000000000000000000−2i22i200
χ574-44-4-44-44000-4-44400000000000000000000000000000000000000000000000022−22
χ584-44-4-44-44000-4-444000000000000000000000000000000000000000000000000−2222
χ594-4-444-4-444-4-40000400000000000000000000022−22−2222000000000000000000000000
χ604-4-444-4-444-4-400004000000000000000000000−222222−22000000000000000000000000
χ614-4-444-4-44-4440000-4000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ624-4-444-4-44-4440000-400000000000000000−2i22i22i2−2i20000000000000000000000000000
χ634-4-44-444-44-44-44-44-40000400-400000000000000000000000000000000000000000
χ644-4-44-444-4-44-4-44-4440000-400400000000000000000000000000000000000000000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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