Finite Group Databasebeta

← Group #98527

Character table — Group #98527

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444442222444444444422448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2-2-222-2-2222222-2-2000022-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-2-2-222-2-20000-2-22222000000000000000000000000
χ19222222222222-2-2-2-2-2-2222222-2-2220000-2-222-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2-2-2-2-222000022-2-222000000000000000000000000
χ2122222222-2-2-2-222-2-22-22-200002-22-2000000000022-2-2002-20000000000000000
χ2222222222-2-2-2-222-2-22-22-200002-22-20000000000-2-22200-220000000000000000
χ2322222222-2-2-2-222-2-2-22-220000-22-22000000000022-2-200-220000000000000000
χ2422222222-2-2-2-222-2-2-22-220000-22-220000000000-2-222002-20000000000000000
χ2522222222-2-2-2-2-2-2222-2-2200002-2-2222-2-200000000002-2000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2200002-2-22-2-2220000000000-22000000000000000000
χ2722222222-2-2-2-2-2-222-222-20000-222-222-2-20000000000-22000000000000000000
χ2822222222-2-2-2-2-2-222-222-20000-222-2-2-22200000000002-2000000000000000000
χ29222-2-22-2-222-2-200002-2002i2i−2i−2i-220000002i−2i00000000000000000000i2−i2i2−i22−22−2
χ30222-2-22-2-222-2-200002-2002i2i−2i−2i-220000002i−2i00000000000000000000−i2i2−i2i2−22−22
χ31222-2-22-2-222-2-200002-200−2i−2i2i2i-22000000−2i2i00000000000000000000i2−i2i2−i2−22−22
χ32222-2-22-2-222-2-200002-200−2i−2i2i2i-22000000−2i2i00000000000000000000−i2i2−i2i22−22−2
χ33222-2-22-2-222-2-20000-22002i2i−2i−2i2-2000000−2i2i000000000000000000002−2−22−i2i2i2−i2
χ34222-2-22-2-222-2-20000-22002i2i−2i−2i2-2000000−2i2i00000000000000000000−222−2i2−i2−i2i2
χ35222-2-22-2-222-2-20000-2200−2i−2i2i2i2-20000002i−2i000000000000000000002−2−22i2−i2−i2i2
χ36222-2-22-2-222-2-20000-2200−2i−2i2i2i2-20000002i−2i00000000000000000000−222−2−i2i2i2−i2
χ372-22-2-2-2222-22-2000000222-22-200-2-20000002-20000000000i2−i2i2−i2i2−i2i2−i200000000
χ382-22-2-2-2222-22-2000000222-22-200-2-20000002-20000000000−i2i2−i2i2−i2i2−i2i200000000
χ392-22-2-2-2222-22-200000022-22-2200-2-2000000-220000000000i2−i2i2−i2−i2i2−i2i200000000
χ402-22-2-2-2222-22-200000022-22-2200-2-2000000-220000000000−i2i2−i2i2i2−i2i2−i200000000
χ412-22-2-2-2222-22-2000000-2-22-22-20022000000-2200000000002−2−222−2−2200000000
χ422-22-2-2-2222-22-2000000-2-22-22-20022000000-220000000000−222−2−222−200000000
χ432-22-2-2-2222-22-2000000-2-2-22-2200220000002-200000000002−2−22−222−200000000
χ442-22-2-2-2222-22-2000000-2-2-22-2200220000002-20000000000−222−22−2−2200000000
χ45444-4-44-4-4-4-444000044000000-4-4000000000000000000000000000000000000
χ46444-4-44-4-4-4-4440000-4-400000044000000000000000000000000000000000000
χ4744-44-4-44-400004-4000000000000000000000000004i−4i00000000000000000000
χ4844-44-4-44-400004-400000000000000000000000000−4i4i00000000000000000000
χ4944-44-4-44-40000-440000000000000000000000004i−4i0000000000000000000000
χ5044-44-4-44-40000-44000000000000000000000000−4i4i0000000000000000000000
χ514-4444-4-4-44-4-44000000004i−4i−4i4i00000000000000000000000000000000000000
χ524-4444-4-4-44-4-4400000000−4i4i4i−4i00000000000000000000000000000000000000
χ534-4444-4-4-4-444-40000000000000000000000004i−4i000000000000000000000000
χ544-4444-4-4-4-444-4000000000000000000000000−4i4i000000000000000000000000
χ554-44-4-4-444-44-440000004-4000000-440000000000000000000000000000000000
χ564-44-4-4-444-44-44000000-440000004-40000000000000000000000000000000000
χ574-4-44-44-440000004-4000000000000004-4000000000000000000000000000000
χ584-4-44-44-440000004-400000000000000-44000000000000000000000000000000
χ594-4-44-44-44000000-440000000000004-400000000000000000000000000000000
χ604-4-44-44-44000000-44000000000000-4400000000000000000000000000000000
χ6188-8-88-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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