Finite Group Databasebeta

← Group #257021

Character table — Group #257021

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
χ311111111111111111111111111111-1-1-1-11111111111111111-11-1-1-1-11-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-111111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-111-11-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-111111-1-1-1-1
χ91111111111-1-1-1-111-1-11-1-111111-11111-1-11111-1-1-1-11111-1-1-1-11-11-11-1-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-11-1-111111-11111-1-1-1-1-1-11111-1-1-1-111111-11-11-1-1-1-1-111-1-111
χ111111111111-1-1-1-111-1-11-1-111111-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-11-11-11-1-111-1-111
χ121111111111-1-1-1-111-1-11-1-111111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-11-11-1111-1-111-1-1
χ131111111111-1-1-1-111-1-11-1-1111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-111-1-111111-1-1-1-111
χ141111111111-1-1-1-111-1-11-1-1111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111-1-1111-1-11111-1-1
χ151111111111-1-1-1-111-1-11-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-111-11-1-1-11111-1-1
χ161111111111-1-1-1-111-1-11-1-1111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-111-11-111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-200-2002222000000000000000000-2-2000000000000
χ18222222222222222222-2-2-2-2-2-200-200-2-2-2-200000000000000000022000000000000
χ192222222222-2-2-2-222-2-2-222-2-2-20020022-2-2000000000000000000-22000000000000
χ202222222222-2-2-2-222-2-2-222-2-2-200200-2-2220000000000000000002-2000000000000
χ2122222222-2-22222-2-2-2-2222-2-2222-2-2-200000000000000000000020000-2000000000
χ2222222222-2-22222-2-2-2-2222-2-22-2-2-222000000000000000000000-200002000000000
χ2322222222-2-22222-2-2-2-2-2-2-222-200200000000000000000000002000-2-20200000000
χ2422222222-2-22222-2-2-2-2-2-2-222-20020000000000000000000000-2000220-200000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2000000000000000000000-200002000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-2-22-2-222200000000000000000000020000-2000000000
χ2722222222-2-2-2-2-2-2-2-222-22222-200-200000000000000000000002000-220-200000000
χ2822222222-2-2-2-2-2-2-2-222-22222-200-20000000000000000000000-20002-20200000000
χ29222-2-22-2-22-200002-200-2002-222i−2i02i−2i000000002i2i−2i−2i000022-2-20000000000000000
χ30222-2-22-2-22-200002-200-2002-222i−2i02i−2i00000000−2i−2i2i2i0000-2-2220000000000000000
χ31222-2-22-2-22-200002-200-2002-22−2i2i0−2i2i000000002i2i−2i−2i0000-2-2220000000000000000
χ32222-2-22-2-22-200002-200-2002-22−2i2i0−2i2i00000000−2i−2i2i2i000022-2-20000000000000000
χ33222-2-22-2-2-220000-2200-200-2222i−2i0−2i2i00002i2i−2i−2i000022-2-200000000000000000000
χ34222-2-22-2-2-220000-2200-200-2222i−2i0−2i2i0000−2i−2i2i2i0000-2-22200000000000000000000
χ35222-2-22-2-2-220000-2200-200-222−2i2i02i−2i00002i2i−2i−2i0000-2-22200000000000000000000
χ36222-2-22-2-2-220000-2200-200-222−2i2i02i−2i0000−2i−2i2i2i000022-2-200000000000000000000
χ372-222-2-2-222222-2-2-2-22-2000000000002i−2i2i−2i00000000i2−i2i2−i2i2−i2i2−i20000000000002−22−2
χ382-222-2-2-222222-2-2-2-22-2000000000002i−2i2i−2i00000000−i2i2−i2i2−i2i2−i2i2000000000000−22−22
χ392-222-2-2-222222-2-2-2-22-200000000000−2i2i−2i2i00000000i2−i2i2−i2i2−i2i2−i2000000000000−22−22
χ402-222-2-2-222222-2-2-2-22-200000000000−2i2i−2i2i00000000−i2i2−i2i2−i2i2−i2i20000000000002−22−2
χ412-222-2-2-2222-2-222-2-2-22000000000002i−2i−2i2i00000000i2−i2i2−i2−i2i2−i2i20000000000002−2−22
χ422-222-2-2-2222-2-222-2-2-22000000000002i−2i−2i2i00000000−i2i2−i2i2i2−i2i2−i2000000000000−222−2
χ432-222-2-2-2222-2-222-2-2-2200000000000−2i2i2i−2i00000000i2−i2i2−i2−i2i2−i2i2000000000000−222−2
χ442-222-2-2-2222-2-222-2-2-2200000000000−2i2i2i−2i00000000−i2i2−i2i2i2−i2i2−i20000000000002−2−22
χ45444-4-44-4-44-400004-400400-44-400000000000000000000000000000000000000000
χ46444-4-44-4-4-440000-44004004-4-400000000000000000000000000000000000000000
χ4744-4-44-4-44004-44-400000000000000000000000000000000000000000002i−2i2i−2i0000
χ4844-4-44-4-44004-44-40000000000000000000000000000000000000000000−2i2i−2i2i0000
χ4944-4-44-4-4400-44-4400000000000000000000000000000000000000000002i−2i−2i2i0000
χ5044-4-44-4-4400-44-440000000000000000000000000000000000000000000−2i2i2i−2i0000
χ514-444-4-4-44-4-444-4-444-4400000000000000000000000000000000000000000000000
χ524-444-4-4-44-4-4-4-444444-400000000000000000000000000000000000000000000000
χ534-44-44-44-44-40000-44000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ544-44-44-44-44-40000-4400000000000000000000000000000−2i22i22i2−2i20000000000000000
χ554-44-44-44-4-4400004-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ564-44-44-44-4-4400004-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ574-4-4444-4-4000000000004-40000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ584-4-4444-4-4000000000004-4000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ594-4-4444-4-400000000000-440000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ604-4-4444-4-400000000000-44000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ614-4-4-4-4444004-4-4400000000000000000002-2-222-2-22000000000000000000000000
χ624-4-4-4-4444004-4-440000000000000000000-222-2-222-2000000000000000000000000
χ634-4-4-4-444400-444-400000000000000000002-2-22-222-2000000000000000000000000
χ644-4-4-4-444400-444-40000000000000000000-222-22-2-22000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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