Finite Group Databasebeta

← Group #258668

Character table — Group #258668

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888884444444444448888
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
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-11-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1
χ91111111111111111-1-1-1-1-1-11111-11111-1-11111-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-11111-11111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-11111-111-1-1111111-1-1-1-1-1-1-1-11111-11-1-111-1-111-1-1-1-111
χ121111111111111111-1-1-1-1-1-11111-111-1-111-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-1111111-1-111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1111-1-11111-1-1-1-111
χ1722222222222-2-2-2-2222-2-2-2-2-2-20020022-2-20000000000000000-2200000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-200200-2-22200000000000000002-200000000000000
χ1922222222222-2-2-2-22-2-22222-2-200-20022220000000000000000-2-200000000000000
χ2022222222222-2-2-2-22-2-22222-2-200-200-2-2-2-200000000000000002200000000000000
χ2122222222-2-2-22222-22222-2-2-2-222-2-2-2000000000000000000000000002-200000000
χ2222222222-2-2-22222-22222-2-2-2-2-2-2-22200000000000000000000000000-2200000000
χ2322222222-2-2-22222-2-2-2-2-222-2-2222-2-200000000000000000000000000-2200000000
χ2422222222-2-2-22222-2-2-2-2-222-2-2-2-2222000000000000000000000000002-200000000
χ2522222222-2-2-2-2-2-2-2-222-2-2222200-20000000000000000000000002-22-20000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2222200-2000000000000000000000000-22-220000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2220020000000000000000000000002-2-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-222002000000000000000000000000-222-20000000000
χ292-2222-2-2-22-2-200002002-22-200000002i−2i2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ302-2222-2-2-22-2-200002002-22-200000002i−2i2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ312-2222-2-2-22-2-200002002-22-20000000−2i2i−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ322-2222-2-2-22-2-200002002-22-20000000−2i2i−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ332-2222-2-2-22-2-20000200-22-2200000002i−2i−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ342-2222-2-2-22-2-20000200-22-2200000002i−2i−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ352-2222-2-2-22-2-20000200-22-220000000−2i2i2i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ362-2222-2-2-22-2-20000200-22-220000000−2i2i2i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-22-2-222-222-22-22-2-2000000-222i−2i02i−2i000000002-22-20000000000000000002i−2i0000
χ382-22-2-222-222-22-22-2-2000000-222i−2i02i−2i00000000-22-22000000000000000000−2i2i0000
χ392-22-2-222-222-22-22-2-2000000-22−2i2i0−2i2i000000002-22-2000000000000000000−2i2i0000
χ402-22-2-222-222-22-22-2-2000000-22−2i2i0−2i2i00000000-22-220000000000000000002i−2i0000
χ412-22-2-222-2-2-222-22-220000002-22i−2i0−2i2i00002i−2i2i−2i000000000000000000002-2000000
χ422-22-2-222-2-2-222-22-220000002-22i−2i0−2i2i0000−2i2i−2i2i00000000000000000000-22000000
χ432-22-2-222-2-2-222-22-220000002-2−2i2i02i−2i00002i−2i2i−2i00000000000000000000-22000000
χ442-22-2-222-2-2-222-22-220000002-2−2i2i02i−2i0000−2i2i−2i2i000000000000000000002-2000000
χ45444-4-4-4-444-440000-400000000000000000000022−22−2222000000000000000000000000
χ46444-4-4-4-444-440000-4000000000000000000000−222222−22000000000000000000000000
χ47444-4-4-4-44-44-400004000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ48444-4-4-4-44-44-40000400000000000000000−2i22i22i2−2i20000000000000000000000000000
χ4944-44-44-4-400044-4-400000000000000000000000000000022−2222−220000000000000000
χ5044-44-44-4-400044-4-4000000000000000000000000000000−2222−22220000000000000000
χ5144-44-44-4-4000-4-444000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5244-44-44-4-4000-4-44400000000000000000000000000−2i22i2−2i22i200000000000000000000
χ534-4444-4-4-4-4440000-4004-4-440000000000000000000000000000000000000000000
χ544-4444-4-4-4-4440000-400-444-40000000000000000000000000000000000000000000
χ554-44-4-444-444-4-44-44-40000004-400000000000000000000000000000000000000000
χ564-44-4-444-4-4-44-44-444000000-4400000000000000000000000000000000000000000
χ574-4-44-4-444000000004i−4i000000000000000000000002-2-222i−2i−2i2i0000000000000000
χ584-4-44-4-444000000004i−4i00000000000000000000000-222-2−2i2i2i−2i0000000000000000
χ594-4-44-4-44400000000−4i4i000000000000000000000002-2-22−2i2i2i−2i0000000000000000
χ604-4-44-4-44400000000−4i4i00000000000000000000000-222-22i−2i−2i2i0000000000000000
χ614-4-4-444-440004-4-440000000000000000000000000000000000000000000000002i2−2i2
χ624-4-4-444-440004-4-44000000000000000000000000000000000000000000000000−2i22i2
χ634-4-4-444-44000-444-400000000000000000000000000000000000000000000002i2−2i200
χ644-4-4-444-44000-444-40000000000000000000000000000000000000000000000−2i22i200
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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