Finite Group Databasebeta

← Group #112413

Character table — Group #112413

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444444444448888888822222244888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ9111111-1-1-111-1-111-1-1-1-1111-11-1-1iiii−i−i−i−i1111-1-1-1-111-1-11-11-1ii−i−iii−i−iii−i−i
χ10111111-1-1-111-1-111-1-1-1-1111-11-1-1iiii−i−i−i−i1111-1-1-1-1-1-111-11-11ii−i−i−i−iii−i−iii
χ11111111-1-1-111-1-111-1-1-1-1111-11-1-1iiii−i−i−i−i-1-1-1-1111111-1-1-11-11−i−iiiii−i−i−i−iii
χ12111111-1-1-111-1-111-1-1-1-1111-11-1-1iiii−i−i−i−i-1-1-1-11111-1-1111-11-1−i−iii−i−iiiii−i−i
χ13111111-1-1-111-1-111-1-1-1-1111-11-1-1−i−i−i−iiiii1111-1-1-1-111-1-11-11-1−i−iii−i−iii−i−iii
χ14111111-1-1-111-1-111-1-1-1-1111-11-1-1−i−i−i−iiiii1111-1-1-1-1-1-111-11-11−i−iiiii−i−iii−i−i
χ15111111-1-1-111-1-111-1-1-1-1111-11-1-1−i−i−i−iiiii-1-1-1-1111111-1-1-11-11ii−i−i−i−iiiii−i−i
χ16111111-1-1-111-1-111-1-1-1-1111-11-1-1−i−i−i−iiiii-1-1-1-11111-1-1111-11-1ii−i−iii−i−i−i−iii
χ17222222222-2-2-2-2-2-2222222-2-2-2-2-200000000000000000000000000002-22-20000
χ18222222222-2-2-2-2-2-2222222-2-2-2-2-20000000000000000000000000000-22-220000
χ1922222222-22222-2-2-2-2-22-2-2-2-222-20000000000000000000000002i−2i2i−2i00000000
χ2022222222-22222-2-2-2-2-22-2-2-2-222-2000000000000000000000000−2i2i−2i2i00000000
χ2122222222-2-2-2-2-222-2-2-22-2-222-2-22000000000000000000002-2-22000000000000
χ2222222222-2-2-2-2-222-2-2-22-2-222-2-2200000000000000000000-222-2000000000000
χ23222222-2-2222-2-2-2-2222-2-2-2-222-220000000000000000000000002-2-2200000000
χ24222222-2-2222-2-2-2-2222-2-2-2-222-22000000000000000000000000-222-200000000
χ25222222-2-22-2-22222222-2-2-22-2-22-20000000000000000000022-2-2000000000000
χ26222222-2-22-2-22222222-2-2-22-2-22-200000000000000000000-2-222000000000000
χ27222222-2-2-2-2-222-2-2-2-2-2-222-22-22200000000000000000000000000002i−2i−2i2i0000
χ28222222-2-2-2-2-222-2-2-2-2-2-222-22-2220000000000000000000000000000−2i2i2i−2i0000
χ292222-2-22222222-2-2-2-22-22-22-2-2-2222-2-222-2-20000000000000000000000000000
χ302222-2-22222222-2-2-2-22-22-22-2-2-22-2-222-2-2220000000000000000000000000000
χ312222-2-2222-2-2-2-222-2-22-22-2-2222-200000000000000002-22-20000000000000000
χ322222-2-2222-2-2-2-222-2-22-22-2-2222-20000000000000000-22-220000000000000000
χ332222-2-222-222222222-2-2-22-22-2-2-20000000022-2-222-2-200000000000000000000
χ342222-2-222-222222222-2-2-22-22-2-2-200000000-2-222-2-22200000000000000000000
χ352222-2-222-2-2-2-2-2-2-222-2-2-222-2222000000000000000000000000000000002-22-2
χ362222-2-222-2-2-2-2-2-2-222-2-2-222-222200000000000000000000000000000000-22-22
χ372222-2-2-2-2222-2-222-2-222-22-2-2-2220000000022-2-2-2-22200000000000000000000
χ382222-2-2-2-2222-2-222-2-222-22-2-2-22200000000-2-22222-2-200000000000000000000
χ392222-2-2-2-22-2-222-2-2-2-222-22222-2-2000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2-22-2-222-2-2-2-222-22222-2-200000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2-2-222-2-2-2-222-222-222-22-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ422222-2-2-2-2-222-2-2-2-222-222-222-22-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ432222-2-2-2-2-2-2-2222222-222-2-2-22-2200000000000000002-2-220000000000000000
χ442222-2-2-2-2-2-2-2222222-222-2-2-22-220000000000000000-222-20000000000000000
χ4544-4-44-40040000004-4-4000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ4644-4-44-40040000004-4-400000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ4744-4-44-400-4000000-444000000002-22-2-22-220000000000000000000000000000
χ4844-4-44-400-4000000-44400000000-22-222-22-20000000000000000000000000000
χ4944-4-4-44004000000-44-4000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ5044-4-4-44004000000-44-400000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ5144-4-4-4400-40000004-44000000002-2-22-222-20000000000000000000000000000
χ5244-4-4-4400-40000004-4400000000-222-22-2-220000000000000000000000000000
χ534-4-44004-404-44-40000000000000000000000022−220022−2200000000000000000000
χ544-4-44004-404-44-400000000000000000000000−222200−222200000000000000000000
χ554-4-44004-40-44-4400000000000000000000022−220022−220000000000000000000000
χ564-4-44004-40-44-44000000000000000000000−222200−22220000000000000000000000
χ574-4-4400-4404-4-440000000000000000000000022−2200−222200000000000000000000
χ584-4-4400-4404-4-4400000000000000000000000−22220022−2200000000000000000000
χ594-4-4400-440-444-400000000000000000000022−2200−22220000000000000000000000
χ604-4-4400-440-444-4000000000000000000000−22220022−220000000000000000000000
χ618-88-80000000008-800000000000000000000000000000000000000000000000
χ628-88-8000000000-8800000000000000000000000000000000000000000000000

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