Finite Group Databasebeta

← Group #98548

Character table — Group #98548

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444444444888888888888881616161616161616161616161616161616161616
order12222222222244444444444444442244444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
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
χ9111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-2222222-2-2-2-222-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2220000000000000000000000000000
χ19222222222222-2-222-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000
χ20222222222222-2-222-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000
χ2122222222-2-2-2-22-22-222-2-200002-22-2000000000022-2-2002-20000000000000000
χ2222222222-2-2-2-22-22-222-2-200002-22-20000000000-2-22200-220000000000000000
χ2322222222-2-2-2-22-2-22-2-22200002-2-2200000022-2-200002-2000000000000000000
χ2422222222-2-2-2-22-2-22-2-22200002-2-22000000-2-2220000-22000000000000000000
χ2522222222-2-2-2-2-222-2-2-2220000-222-200000022-2-20000-22000000000000000000
χ2622222222-2-2-2-2-222-2-2-2220000-222-2000000-2-22200002-2000000000000000000
χ2722222222-2-2-2-2-22-2222-2-20000-22-22000000000022-2-200-220000000000000000
χ2822222222-2-2-2-2-22-2222-2-20000-22-220000000000-2-222002-20000000000000000
χ29222-2-2-22-222-2-2002-200002i2i−2i−2i00-2200002i−2i000000000000i2−i2i2−i22−22−200000000
χ30222-2-2-22-222-2-2002-200002i2i−2i−2i00-2200002i−2i000000000000−i2i2−i2i2−22−2200000000
χ31222-2-2-22-222-2-2002-20000−2i−2i2i2i00-220000−2i2i000000000000i2−i2i2−i2−22−2200000000
χ32222-2-2-22-222-2-2002-20000−2i−2i2i2i00-220000−2i2i000000000000−i2i2−i2i22−22−200000000
χ33222-2-2-22-222-2-200-2200002i2i−2i−2i002-20000−2i2i0000000000002−2−22−i2i2i2−i200000000
χ34222-2-2-22-222-2-200-2200002i2i−2i−2i002-20000−2i2i000000000000−222−2i2−i2−i2i200000000
χ35222-2-2-22-222-2-200-220000−2i−2i2i2i002-200002i−2i0000000000002−2−22i2−i2−i2i200000000
χ36222-2-2-22-222-2-200-220000−2i−2i2i2i002-200002i−2i000000000000−222−2−i2i2i2−i200000000
χ372-2-222-22-22-22-22-20000002i−2i2i−2i-2200002i−2i00000000000000000000002−22−2i2−i2i2−i2
χ382-2-222-22-22-22-22-20000002i−2i2i−2i-2200002i−2i0000000000000000000000−22−22−i2i2−i2i2
χ392-2-222-22-22-22-22-2000000−2i2i−2i2i-220000−2i2i00000000000000000000002−22−2−i2i2−i2i2
χ402-2-222-22-22-22-22-2000000−2i2i−2i2i-220000−2i2i0000000000000000000000−22−22i2−i2i2−i2
χ412-2-222-22-22-22-2-220000002i−2i2i−2i2-20000−2i2i0000000000000000000000i2−i2−i2i2−222−2
χ422-2-222-22-22-22-2-220000002i−2i2i−2i2-20000−2i2i0000000000000000000000−i2i2i2−i22−2−22
χ432-2-222-22-22-22-2-22000000−2i2i−2i2i2-200002i−2i0000000000000000000000i2−i2−i2i22−2−22
χ442-2-222-22-22-22-2-22000000−2i2i−2i2i2-200002i−2i0000000000000000000000−i2i2i2−i2−222−2
χ45444-4-4-44-4-4-44400440000000000-4-40000000000000000000000000000000000
χ46444-4-4-44-4-4-44400-4-40000000000440000000000000000000000000000000000
χ4744-44-4-4-44000000004-400000000000000000000004i−4i00000000000000000000
χ4844-44-4-4-44000000004-40000000000000000000000−4i4i00000000000000000000
χ4944-44-4-4-4400000000-44000000000000000000004i−4i0000000000000000000000
χ5044-44-4-4-4400000000-4400000000000000000000−4i4i0000000000000000000000
χ514-44-44-4-4400000000004-400000000000000004i−4i000000000000000000000000
χ524-44-44-4-4400000000004-40000000000000000−4i4i000000000000000000000000
χ534-44-44-4-440000000000-44000000000000004i−4i00000000000000000000000000
χ544-44-44-4-440000000000-4400000000000000−4i4i00000000000000000000000000
χ554-4-444-44-4-44-44440000000000-4-4000000000000000000000000000000000000
χ564-4-444-44-4-44-44-4-4000000000044000000000000000000000000000000000000
χ574-4-4-4-44444-4-44000000004-4-4400000000000000000000000000000000000000
χ584-4-4-4-44444-4-4400000000-444-400000000000000000000000000000000000000
χ594-4-4-4-4444-444-400000000000000004-400000000000000000000000000000000
χ604-4-4-4-4444-444-40000000000000000-4400000000000000000000000000000000
χ6188-8-888-8-8000000000000000000000000000000000000000000000000000000
χ628-888-88-8-8000000000000000000000000000000000000000000000000000000

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