Finite Group Databasebeta

← Group #167503

Character table — Group #167503

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444444444444444444444488888888888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-11-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ7111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-1111-1-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-111-1-1111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-11-11-1-1-11-111-1-111
χ1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1111-11-1-1-1-111
χ1211111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1-11-1-1-111111-1-1
χ1311111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-1-11-111-1-111
χ1411111111-1-1-1-1-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-11-11-11111-1-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111-1-1
χ1611111111-1-1-1-1-1-1-1-111-1-11111-1-1-111-1-111-1-1-1-111111111-1-1-1-11-1-111-111-11-1-1-1-111
χ1722222222222222222-2-2-2-22-2-222-2220000000000000000000000-2-2000000000000
χ1822222222222222222-2-2-2-22-2-2-2-2-2-2-2000000000000000000000022000000000000
χ19222222222222-2-2-2-2-2222-2-22-200-200000000000000000000002-200-220000000000
χ20222222222222-2-2-2-2-2222-2-22-200-20000000000000000000000-22002-20000000000
χ21222222222222-2-2-2-2-2-2-2-22-2-220020022-2-2000000000000000000000000-22000000
χ22222222222222-2-2-2-2-2-2-2-22-2-2200200-2-2220000000000000000000000002-2000000
χ2322222222-2-2-2-22222-22-2-2-2-22-200200000000000000000000002200-2-20000000000
χ2422222222-2-2-2-22222-22-2-2-2-22-20020000000000000000000000-2-200220000000000
χ2522222222-2-2-2-22222-2-2222-2-2200-2002222000000000000000000000000-2-2000000
χ2622222222-2-2-2-22222-2-2222-2-2200-200-2-2-2-200000000000000000000000022000000
χ2722222222-2-2-2-2-2-2-2-22-222-22-2-2222-2-20000000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-22-222-22-2-2-2-222200000000000000000000002-2000000000000
χ29222-22-2-2-222-2-222-2-2-200002002i−2i02i−2i000000000000i2i2−i2−i2i2i2−i2−i20000000000002−22−2
χ30222-22-2-2-222-2-222-2-2-200002002i−2i02i−2i000000000000−i2−i2i2i2−i2−i2i2i2000000000000−22−22
χ31222-22-2-2-222-2-222-2-2-20000200−2i2i0−2i2i000000000000i2i2−i2−i2i2i2−i2−i2000000000000−22−22
χ32222-22-2-2-222-2-222-2-2-20000200−2i2i0−2i2i000000000000−i2−i2i2i2−i2−i2i2i20000000000002−22−2
χ33222-22-2-2-2-2-222-2-222-200002002i−2i0−2i2i000000000000i2i2−i2−i2−i2−i2i2i20000000000002−2−22
χ34222-22-2-2-2-2-222-2-222-200002002i−2i0−2i2i000000000000−i2−i2i2i2i2i2−i2−i2000000000000−222−2
χ35222-22-2-2-2-2-222-2-222-20000200−2i2i02i−2i000000000000i2i2−i2−i2−i2−i2i2i2000000000000−222−2
χ36222-22-2-2-2-2-222-2-222-20000200−2i2i02i−2i000000000000−i2−i2i2i2i2i2−i2−i20000000000002−2−22
χ372-2-2-222-2200002-22-2002-2200-2000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i22−22−22−22−20000000000000000
χ382-2-2-222-2200002-22-2002-2200-2000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2−22−22−22−220000000000000000
χ392-2-2-222-2200002-22-2002-2200-200000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2−22−22−22−220000000000000000
χ402-2-2-222-2200002-22-2002-2200-200000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i22−22−22−22−20000000000000000
χ412-2-2-222-220000-22-2200-22200-2000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i22−22−2−22−220000000000000000
χ422-2-2-222-220000-22-2200-22200-2000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−22−222−22−20000000000000000
χ432-2-2-222-220000-22-2200-22200-200000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−22−222−22−20000000000000000
χ442-2-2-222-220000-22-2200-22200-200000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i22−22−2−22−220000000000000000
χ45444-44-4-4-444-4-4-4-44440000-40000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-44444-4-440000-40000000000000000000000000000000000000000000
χ4744-44-44-4-400000000040000-4000000000022−2222−220000000000000000000000000000
χ4844-44-44-4-400000000040000-40000000000−2222−22220000000000000000000000000000
χ4944-44-44-4-4000000000-400004000000000000002i2−2i22i2−2i2000000000000000000000000
χ5044-44-44-4-4000000000-40000400000000000000−2i22i2−2i22i2000000000000000000000000
χ514-444-4-4-444i−4i4i−4i00000000000000000000000000000000000000000002i−2i002-20000
χ524-444-4-4-444i−4i4i−4i0000000000000000000000000000000000000000000−2i2i00-220000
χ534-444-4-4-44−4i4i−4i4i00000000000000000000000000000000000000000002i−2i00-220000
χ544-444-4-4-44−4i4i−4i4i0000000000000000000000000000000000000000000−2i2i002-20000
χ554-44-4-444-44i−4i−4i4i0000000000000000000002i−2i−2i2i2-2-22000000000000000000000000
χ564-44-4-444-44i−4i−4i4i000000000000000000000−2i2i2i−2i-222-2000000000000000000000000
χ574-44-4-444-4−4i4i4i−4i0000000000000000000002i−2i−2i2i-222-2000000000000000000000000
χ584-44-4-444-4−4i4i4i−4i000000000000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ594-4-444-44-400004-4-4400000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ604-4-444-44-400004-4-440000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ614-4-444-44-40000-444-400000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ624-4-444-44-40000-444-40000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ634-4-4-444-4400004-44-400-44-400400000000000000000000000000000000000000000
χ644-4-4-444-440000-44-44004-4-400400000000000000000000000000000000000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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