Finite Group Databasebeta

← Group #287916

Character table — Group #287916

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-111111111-1-111-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-11-1-1-11-11111-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-1111-1-1-1-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-11-1-1-1111-1-111-11
χ1211111111-1-1-1-111111111-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1111-11-1-111-1-11-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1111-11-1-111-1-1-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-11-1-1-1111-1-1111-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-1111-1-1-1-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111-1-1-11-11111-1-1-11
χ1722222222222222-22-2-2-22-2-2-2-222-20000000000000000000000002200-2-200000000
χ1822222222222222-22-2-2-22-2-2-2-222-2000000000000000000000000-2-2002200000000
χ19222222222222-2-22-2222-222-2-2-2-2-20000222200000000-2-2-2-2000000000000000000
χ20222222222222-2-22-2222-222-2-2-2-2-20000-2-2-2-2000000002222000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-222i2i−2i−2i000000002i2i−2i−2i0000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-22−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000
χ2322222222-2-2-2-222-22-2-2-2222-2-2-2-220000000000000000000000002-200-2200000000
χ2422222222-2-2-2-222-22-2-2-2222-2-2-2-22000000000000000000000000-22002-200000000
χ2522222222-2-2-2-2-2-22-2222-2-2-2-2-2222000022-2-200000000-2-222000000000000000000
χ2622222222-2-2-2-2-2-22-2222-2-2-2-2-22220000-2-2220000000022-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-22i2i−2i−2i00000000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000
χ29222-2-2-22-222-2-200-202-2202-20000000002i−2i2i−2ii2i2−i2−i200000000i2i2−i2−i2000000002−22−200
χ30222-2-2-22-222-2-200-202-2202-20000000002i−2i2i−2i−i2−i2i2i200000000−i2−i2i2i200000000−22−2200
χ31222-2-2-22-222-2-200-202-2202-2000000000−2i2i−2i2ii2i2−i2−i200000000i2i2−i2−i200000000−22−2200
χ32222-2-2-22-222-2-200-202-2202-2000000000−2i2i−2i2i−i2−i2i2i200000000−i2−i2i2i2000000002−22−200
χ33222-2-2-22-2-2-22200-202-220-220000000002i−2i−2i2ii2i2−i2−i200000000−i2−i2i2i2000000002−2−2200
χ34222-2-2-22-2-2-22200-202-220-220000000002i−2i−2i2i−i2−i2i2i200000000i2i2−i2−i200000000−222−200
χ35222-2-2-22-2-2-22200-202-220-22000000000−2i2i2i−2ii2i2−i2−i200000000−i2−i2i2i200000000−222−200
χ36222-2-2-22-2-2-22200-202-220-22000000000−2i2i2i−2i−i2−i2i2i200000000i2i2−i2−i2000000002−2−2200
χ372-2-2-22-22200002-2222-2-2-2002-2000000000002-22-22i−2i2i−2i00000000002i−2i0000000000
χ382-2-2-22-22200002-2222-2-2-2002-2000000000002-22-2−2i2i−2i2i0000000000−2i2i0000000000
χ392-2-2-22-22200002-2222-2-2-2002-200000000000-22-222i−2i2i−2i0000000000−2i2i0000000000
χ402-2-2-22-22200002-2222-2-2-2002-200000000000-22-22−2i2i−2i2i00000000002i−2i0000000000
χ412-2-2-22-2220000-22-2-2-2222002-20000000000000002-2-2200002-22-20000002-2000000
χ422-2-2-22-2220000-22-2-2-2222002-20000000000000002-2-220000-22-22000000-22000000
χ432-2-2-22-2220000-22-2-2-2222002-2000000000000000-222-200002-22-2000000-22000000
χ442-2-2-22-2220000-22-2-2-2222002-2000000000000000-222-20000-22-220000002-2000000
χ45444-4-4-44-444-4-40040-44-40-440000000000000000000000000000000000000000000
χ46444-4-4-44-4-4-4440040-44-404-40000000000000000000000000000000000000000000
χ4744-444-4-4-44-44-4000000000000000000000000000000022−2222−22000000000000000000
χ4844-444-4-4-44-44-40000000000000000000000000000000−2222−2222000000000000000000
χ4944-444-4-4-4-44-44000000000000000000000000000000022−22−2222000000000000000000
χ5044-444-4-4-4-44-440000000000000000000000000000000−222222−22000000000000000000
χ5144-4-4-44-444-4-44440-4000-400004-4000000000000000000000000000000000000000
χ5244-4-4-44-444-4-44-4-40400040000-44000000000000000000000000000000000000000
χ5344-4-4-44-44-444-4440-4000-40000-44000000000000000000000000000000000000000
χ5444-4-4-44-44-444-4-4-404000400004-4000000000000000000000000000000000000000
χ554-444-4-4-4400004-40-4000400000002i2−2i22i2−2i20000000000000000000000000000000000
χ564-444-4-4-4400004-40-400040000000−2i22i2−2i22i20000000000000000000000000000000000
χ574-444-4-4-440000-4404000-4000000022−22−22220000000000000000000000000000000000
χ584-444-4-4-440000-4404000-40000000−222222−220000000000000000000000000000000000
χ594-4-44-444-400000040-4-4400000000000000000000000000002i2−2i2−2i22i200000000000000
χ604-4-44-444-400000040-4-440000000000000000000000000000−2i22i22i2−2i200000000000000
χ614-4-44-444-4000000-4044-400000000000000002i2−2i2−2i22i200000000000000000000000000
χ624-4-44-444-4000000-4044-40000000000000000−2i22i22i2−2i200000000000000000000000000
χ634-4-4-44-44400004-4-44-444-400-4400000000000000000000000000000000000000000
χ644-4-4-44-4440000-444-44-4-4400-4400000000000000000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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