Finite Group Databasebeta

← Group #293308

Character table — Group #293308

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444444444888888884444444444448888
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
χ31111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-11111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-111-1111111-1-1-1-11111-1-1-1-1-11-11-11-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-11111-1-1-1-11111-11-11-11-1-1-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11-111-1111-1-1-1-111
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-111-11-1-11111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-11111-1111111-1-1-1-11111-1-1-1-1-1-11-11-11-1-1-111-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-11111-111-1-1-1-11111-1-1-1-11111-1-11-11-11-111-1-111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-11-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11-1-11111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2222200-200000000000000000000000-2-2000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-200-20000000000000000000000022000000000
χ19222222222222-2-2-2-2-2-222-2-2-2-222-2-200200000000000000000000000-22000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-2-2-222002000000000000000000000002-2000000000
χ2122222222-2-2-2-22222-2-222-222-2000000-2000000000000000000022-2-200000000000
χ2222222222-2-2-2-22222-2-222-222-2000000-20000000000000000000-2-22200000000000
χ2322222222-2-2-2-22222-2-2-2-22-2-220000222-2-200000000000000002000000-200000000
χ2422222222-2-2-2-22222-2-2-2-22-2-220000-2-22220000000000000000-2000000200000000
χ2522222222-2-2-2-2-2-2-2-222222-2-22000022-2-2-20000000000000000-2000000200000000
χ2622222222-2-2-2-2-2-2-2-222222-2-220000-2-2-22200000000000000002000000-200000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-222-2000000200000000000000000002-2-2200000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-222-200000020000000000000000000-222-200000000000
χ29222-22-2-2-222-2-222-2-22-20000002-22-2000000000000022−2−222−2−20000000000002−22−2
χ30222-22-2-2-222-2-222-2-22-20000002-22-20000000000000−2−222−2−222000000000000−22−22
χ31222-22-2-2-222-2-222-2-22-2000000-22-22000000000000022−2−222−2−2000000000000−22−22
χ32222-22-2-2-222-2-222-2-22-2000000-22-220000000000000−2−222−2−2220000000000002−22−2
χ33222-22-2-2-222-2-2-2-222-220000002-2-22000000000000022−2−2−2−2220000000000002−2−22
χ34222-22-2-2-222-2-2-2-222-220000002-2-220000000000000−2−22222−2−2000000000000−222−2
χ35222-22-2-2-222-2-2-2-222-22000000-222-2000000000000022−2−2−2−222000000000000−222−2
χ36222-22-2-2-222-2-2-2-222-22000000-222-20000000000000−2−22222−2−20000000000002−2−22
χ372-2-222-2-222-22-20000000022-2-200002i−2i02i−2i000022-2-200002i−2i2i−2i0000000000000000
χ382-2-222-2-222-22-20000000022-2-200002i−2i02i−2i0000-2-2220000−2i2i−2i2i0000000000000000
χ392-2-222-2-222-22-20000000022-2-20000−2i2i0−2i2i000022-2-20000−2i2i−2i2i0000000000000000
χ402-2-222-2-222-22-20000000022-2-20000−2i2i0−2i2i0000-2-22200002i−2i2i−2i0000000000000000
χ412-2-222-2-22-22-22000000002-22-200002i−2i0−2i2i22-2-200002i−2i2i−2i00000000000000000000
χ422-2-222-2-22-22-22000000002-22-200002i−2i0−2i2i-2-2220000−2i2i−2i2i00000000000000000000
χ432-2-222-2-22-22-22000000002-22-20000−2i2i02i−2i22-2-20000−2i2i−2i2i00000000000000000000
χ442-2-222-2-22-22-22000000002-22-20000−2i2i02i−2i-2-22200002i−2i2i−2i00000000000000000000
χ45444-44-4-4-4-4-44444-4-4-4400000000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-444-4-4444-400000000000000000000000000000000000000000000000
χ4744-44-4-44-400000000004-400000000000002-22-22-22-2000000000000000000000000
χ4844-44-4-44-400000000004-40000000000000-22-22-22-22000000000000000000000000
χ4944-44-4-44-40000000000-4400000000000002-22-2-22-22000000000000000000000000
χ5044-44-4-44-40000000000-440000000000000-22-222-22-2000000000000000000000000
χ514-444-44-4-400004-44-4000000000000000002-2-222-2-22000000000000000000000000
χ524-444-44-4-400004-44-400000000000000000-222-2-222-2000000000000000000000000
χ534-444-44-4-40000-44-44000000000000000002-2-22-222-2000000000000000000000000
χ544-444-44-4-40000-44-4400000000000000000-222-22-2-22000000000000000000000000
χ554-44-4-4-44400004-4-44000000000000000000000000000000000000000002-22-20000
χ564-44-4-4-44400004-4-4400000000000000000000000000000000000000000-22-220000
χ574-44-4-4-4440000-444-4000000000000000000000000000000000000000002-2-220000
χ584-44-4-4-4440000-444-400000000000000000000000000000000000000000-222-20000
χ594-4-444-4-444-44-400000000-4-44400000000000000000000000000000000000000000
χ604-4-444-4-44-44-4400000000-44-4400000000000000000000000000000000000000000
χ614-4-4-4444-44-4-440000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ624-4-4-4444-44-4-44000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ634-4-4-4444-4-444-4000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ644-4-4-4444-4-444-400000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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