Finite Group Databasebeta

← Group #265654

Character table — Group #265654

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422444444444444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111111-1-111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ5111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-11-1-11-1111111-1-1-1-1
χ9111111111111-1-1-1-11-1-1-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-11-1-1-11-11-111-1-111-1-1
χ10111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-1-1111111-1-1-1-1-11-11-1-1-11-1-111-1-111
χ11111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-11111-1-1-1-1-1-111111-1-1-11-11-1-1-111-1-111
χ12111111111111-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1111111-1-1-1-11111-11-11-1-1-1111-1-111-1-1
χ13111111111111-1-1-1-11-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1111-1-1-1-111
χ14111111111111-1-1-1-11-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-111111-1-1-11111-1-1
χ15111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-111-11111-1-11111-1-1-1-1111-1-11-11-1-11111-1-1
χ16111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111-111-1-1-1-111
χ172222222222222222-222-2-2-2-2-20000000022-200002200000000-200-2000000000000
χ182222222222222222-222-2-2-2-2-200000000-2-2-20000-2-2000000002002000000000000
χ19222222222222-2-2-2-2-2-2-222-2-2-2000000002220000-2-200000000-2002000000000000
χ20222222222222-2-2-2-2-2-2-222-2-2-200000000-2-2200002200000000200-2000000000000
χ2122222222-2-2-2-222222-2-2-2-2-2-220000000000200000000000000020020-2-200000000
χ2222222222-2-2-2-222222-2-2-2-2-2-2200000000002000000000000000-200-202200000000
χ2322222222-2-2-2-22222-2-2-22222-222-2-2000000-20000000000000000-20020000000000
χ2422222222-2-2-2-22222-2-2-22222-2-2-222000000-20000000000000000200-20000000000
χ2522222222-2-2-2-2-2-2-2-222222-2-220000000000-2000000000000000200-202-200000000
χ2622222222-2-2-2-2-2-2-2-222222-2-220000000000-2000000000000000-20020-2200000000
χ2722222222-2-2-2-2-2-2-2-2-222-2-222-222-2-200000020000000000000000200-20000000000
χ2822222222-2-2-2-2-2-2-2-2-222-2-222-2-2-22200000020000000000000000-20020000000000
χ29222-22-2-2-222-2-20000200002-2-22-22-222-2-200000000022-2-200000000000000000000
χ30222-22-2-2-222-2-20000200002-2-22-22-2-2-222000000000-2-22200000000000000000000
χ31222-22-2-2-222-2-20000200002-2-2-22-2222-2-2000000000-2-22200000000000000000000
χ32222-22-2-2-222-2-20000200002-2-2-22-22-2-22200000000022-2-200000000000000000000
χ33222-22-2-2-2-2-2220000-200002-222-2-2200000002i2i−2i−2i0000002i2i−2i−2i0000000000000000
χ34222-22-2-2-2-2-2220000-200002-222-2-220000000−2i−2i2i2i000000−2i−2i2i2i0000000000000000
χ35222-22-2-2-2-2-2220000-200002-22-222-200000002i2i−2i−2i000000−2i−2i2i2i0000000000000000
χ36222-22-2-2-2-2-2220000-200002-22-222-20000000−2i−2i2i2i0000002i2i−2i−2i0000000000000000
χ372-222-2-2-222-22-22i2i−2i−2i02i−2i00000000000002i−2i000002-2i2−i2i2−i22−22−20000000000002−2i2−i2
χ382-222-2-2-222-22-22i2i−2i−2i02i−2i00000000000002i−2i000002-2−i2i2−i2i2−22−22000000000000−22−i2i2
χ392-222-2-2-222-22-22i2i−2i−2i02i−2i0000000000000−2i2i00000-22i2−i2i2−i22−22−2000000000000−22−i2i2
χ402-222-2-2-222-22-22i2i−2i−2i02i−2i0000000000000−2i2i00000-22−i2i2−i2i2−22−220000000000002−2i2−i2
χ412-222-2-2-222-22-2−2i−2i2i2i0−2i2i00000000000002i−2i00000-22i2−i2i2−i2−22−220000000000002−2−i2i2
χ422-222-2-2-222-22-2−2i−2i2i2i0−2i2i00000000000002i−2i00000-22−i2i2−i2i22−22−2000000000000−22i2−i2
χ432-222-2-2-222-22-2−2i−2i2i2i0−2i2i0000000000000−2i2i000002-2i2−i2i2−i2−22−22000000000000−22i2−i2
χ442-222-2-2-222-22-2−2i−2i2i2i0−2i2i0000000000000−2i2i000002-2−i2i2−i2i22−22−20000000000002−2−i2i2
χ45444-44-4-4-444-4-40000-40000-44400000000000000000000000000000000000000000
χ46444-44-4-4-4-4-444000040000-44-400000000000000000000000000000000000000000
χ4744-4-4-44-4400004i−4i4i−4i000000000000000000000000000000000000000002-22i−2i0000
χ4844-4-4-44-4400004i−4i4i−4i00000000000000000000000000000000000000000-22−2i2i0000
χ4944-4-4-44-440000−4i4i−4i4i000000000000000000000000000000000000000002-2−2i2i0000
χ5044-4-4-44-440000−4i4i−4i4i00000000000000000000000000000000000000000-222i−2i0000
χ514-444-4-4-44-44-444i4i−4i−4i0−4i4i0000000000000000000000000000000000000000000000
χ524-444-4-4-44-44-44−4i−4i4i4i04i−4i0000000000000000000000000000000000000000000000
χ534-44-4-444-44-4-44000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ544-44-4-444-44-4-4400000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ554-44-4-444-4-444-40000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ564-44-4-444-4-444-4000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ574-4-4444-4-4000000000004i−4i00000002-22-20002i−2i2i−2i00000000000000000000000000
χ584-4-4444-4-4000000000004i−4i0000000-22-22000−2i2i−2i2i00000000000000000000000000
χ594-4-4444-4-400000000000−4i4i00000002-22-2000−2i2i−2i2i00000000000000000000000000
χ604-4-4444-4-400000000000−4i4i0000000-22-220002i−2i2i−2i00000000000000000000000000
χ614-4-4-44-44400004-4-440000000000002-2-220002-2-2200000000000000000000000000
χ624-4-4-44-44400004-4-44000000000000-222-2000-222-200000000000000000000000000
χ634-4-4-44-4440000-444-40000000000002-2-22000-222-200000000000000000000000000
χ644-4-4-44-4440000-444-4000000000000-222-20002-2-2200000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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