Finite Group Databasebeta

← Group #98538

Character table — Group #98538

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-2222222-2-222-2-2-2-20000-2-222000000000000000000000000
χ18222222222222-2-2-2-22222-2-222-2-222-2-2000022-2-2000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-222-2-222-2-222000022-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-222-2-222220000-2-222000000000000000000000000
χ2122222222-2-2-2-222-2-200002-22-22-22-2000000000022-2-2002-20000000000000000
χ2222222222-2-2-2-222-2-200002-22-22-22-20000000000-2-22200-220000000000000000
χ2322222222-2-2-2-222-2-20000-22-22-22-22000000000022-2-200-220000000000000000
χ2422222222-2-2-2-222-2-20000-22-22-22-220000000000-2-222002-20000000000000000
χ2522222222-2-2-2-2-2-22200002-2-222-2-220022-2-2000000002-2000000000000000000
χ2622222222-2-2-2-2-2-22200002-2-222-2-2200-2-22200000000-22000000000000000000
χ2722222222-2-2-2-2-2-2220000-222-2-222-20022-2-200000000-22000000000000000000
χ2822222222-2-2-2-2-2-2220000-222-2-222-200-2-222000000002-2000000000000000000
χ29222-2-2-2-2222-2-200002i2i−2i−2i002-200-220000002i−2i0000000000i2−i22−2i2−i22−200000000
χ30222-2-2-2-2222-2-200002i2i−2i−2i002-200-220000002i−2i0000000000−i2i2−22−i2i2−2200000000
χ31222-2-2-2-2222-2-200002i2i−2i−2i00-22002-2000000−2i2i00000000002−2−i2i2−22i2−i200000000
χ32222-2-2-2-2222-2-200002i2i−2i−2i00-22002-2000000−2i2i0000000000−22i2−i22−2−i2i200000000
χ33222-2-2-2-2222-2-20000−2i−2i2i2i002-200-22000000−2i2i0000000000i2−i2−22i2−i2−2200000000
χ34222-2-2-2-2222-2-20000−2i−2i2i2i002-200-22000000−2i2i0000000000−i2i22−2−i2i22−200000000
χ35222-2-2-2-2222-2-20000−2i−2i2i2i00-22002-20000002i−2i00000000002−2i2−i2−22−i2i200000000
χ36222-2-2-2-2222-2-20000−2i−2i2i2i00-22002-20000002i−2i0000000000−22−i2i22−2i2−i200000000
χ372-22-2-222-22-22-200002i−2i2i−2i2-200-2200000000002i−2i0000000000000000i2−i22−2i2−i22−2
χ382-22-2-222-22-22-200002i−2i2i−2i2-200-2200000000002i−2i0000000000000000−i2i2−22−i2i2−22
χ392-22-2-222-22-22-200002i−2i2i−2i-22002-20000000000−2i2i00000000000000002−2−i2i2−22i2−i2
χ402-22-2-222-22-22-200002i−2i2i−2i-22002-20000000000−2i2i0000000000000000−22i2−i22−2−i2i2
χ412-22-2-222-22-22-20000−2i2i−2i2i2-200-220000000000−2i2i0000000000000000i2−i2−22i2−i2−22
χ422-22-2-222-22-22-20000−2i2i−2i2i2-200-220000000000−2i2i0000000000000000−i2i22−2−i2i22−2
χ432-22-2-222-22-22-20000−2i2i−2i2i-22002-200000000002i−2i00000000000000002−2i2−i2−22−i2i2
χ442-22-2-222-22-22-20000−2i2i−2i2i-22002-200000000002i−2i0000000000000000−22−i2i22−2i2−i2
χ45444-4-4-4-44-4-44400000000004400-4-40000000000000000000000000000000000
χ46444-4-4-4-44-4-4440000000000-4-400440000000000000000000000000000000000
χ4744-44-44-4-40000004-400000000000000004-40000000000000000000000000000
χ4844-44-44-4-40000004-40000000000000000-440000000000000000000000000000
χ4944-44-44-4-4000000-44000000000000004-4000000000000000000000000000000
χ5044-44-44-4-4000000-4400000000000000-44000000000000000000000000000000
χ514-4444-4-4-44-4-4400004-4-44000000000000000000000000000000000000000000
χ524-4444-4-4-44-4-440000-444-4000000000000000000000000000000000000000000
χ534-4444-4-4-4-444-400000000000000004-400000000000000000000000000000000
χ544-4444-4-4-4-444-40000000000000000-4400000000000000000000000000000000
χ554-44-4-444-4-44-44000000004400-4-4000000000000000000000000000000000000
χ564-44-4-444-4-44-4400000000-4-40044000000000000000000000000000000000000
χ574-4-44-4-44400004-4000000000000000000000000004-400000000000000000000
χ584-4-44-4-44400004-400000000000000000000000000-4400000000000000000000
χ594-4-44-4-4440000-440000000000000000000000004-40000000000000000000000
χ604-4-44-4-4440000-44000000000000000000000000-440000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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