Finite Group Databasebeta

← Group #116179

Character table — Group #116179

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444444444448888888822448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1iiii−i−i−i−i-11-11−i−iiiii−i−i−i−iii-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii−i−iii11-1-1
χ1211111111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1−i−i−i−iiiii-11-11ii−i−i−i−iiiii−i−i-1-111
χ1311111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-11111iiii−i−i−i−i1-11-1−i−iii−i−iiiii−i−i-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i−i−iii−i−iii11-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−iii−i−i−i−iii-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-11111−i−i−i−iiiii-11-11−i−iiiii−i−iii−i−i11-1-1
χ172222222222-2-2-22222-22-2-2-22-2-2-20000000000000000000000002-22-200000000
χ182222222222-2-2-22222-22-2-2-22-2-2-2000000000000000000000000-22-2200000000
χ1922222222-2-2222-2-2-2-222-2-2-2-222-20000000000000000000000002i−2i−2i2i00000000
χ2022222222-2-2222-2-2-2-222-2-2-2-222-2000000000000000000000000−2i2i2i−2i00000000
χ21222222-2-22222-2-2-2-2-2-2-222-222-2-200000000000000002-2-220000000000000000
χ22222222-2-22222-2-2-2-2-2-2-222-222-2-20000000000000000-222-20000000000000000
χ23222222-2-222-2-22-2-2-2-22-2-2-222-222000000000000000000002i−2i2i−2i000000000000
χ24222222-2-222-2-22-2-2-2-22-2-2-222-22200000000000000000000−2i2i−2i2i000000000000
χ25222222-2-2-2-222-22222-2-2-2-22-22-22000000000000000000002-2-22000000000000
χ26222222-2-2-2-222-22222-2-2-2-22-22-2200000000000000000000-222-2000000000000
χ27222222-2-2-2-2-2-2222222-222-2-2-22-2000000000000000022-2-20000000000000000
χ28222222-2-2-2-2-2-2222222-222-2-2-22-20000000000000000-2-2220000000000000000
χ292222-2-22222222-2-2222-22-22-2-2-2-20000000022-2-222-2-200000000000000000000
χ302222-2-22222222-2-2222-22-22-2-2-2-200000000-2-222-2-22200000000000000000000
χ312222-2-22222-2-2-2-2-222-2-2-22-2-222222-2-222-2-20000000000000000000000000000
χ322222-2-22222-2-2-2-2-222-2-2-22-2-2222-2-222-2-2220000000000000000000000000000
χ332222-2-222-2-222222-2-22-2-22-22-2-2222-2-2-2-2220000000000000000000000000000
χ342222-2-222-2-222222-2-22-2-22-22-2-22-2-22222-2-20000000000000000000000000000
χ352222-2-222-2-2-2-2-222-2-2-2-22-22222-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ362222-2-222-2-2-2-2-222-2-2-2-22-22222-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ372222-2-2-2-22222-222-2-2-222-2-2-2-22200000000000000000000000000002i−2i2i−2i0000
χ382222-2-2-2-22222-222-2-2-222-2-2-2-2220000000000000000000000000000−2i2i−2i2i0000
χ392222-2-2-2-222-2-2222-2-222-222-22-2-2000000000000000000000000000000002i−2i2i−2i
χ402222-2-2-2-222-2-2222-2-222-222-22-2-200000000000000000000000000000000−2i2i−2i2i
χ412222-2-2-2-2-2-222-2-2-222-22-2222-22-2000000000000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-2-222-2-2-222-22-2222-22-200000000000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-2-2-2-22-2-222222-2-222-2200000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-2-2-22-2-222222-2-222-220000000000000000000000000000-222-20000
χ4544-4-44-400000004-44-40000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ4644-4-44-400000004-44-4000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ4744-4-44-40000000-44-440000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ4844-4-44-40000000-44-44000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ4944-4-4-4400000004-4-440000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ5044-4-4-4400000004-4-44000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ5144-4-4-440000000-444-40000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ5244-4-4-440000000-444-4000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ534-4-44004-4004-440000-40000000000000000002i2−2i2002i2−2i200000000000000000000
χ544-4-44004-4004-440000-4000000000000000000−2i22i200−2i22i200000000000000000000
χ554-4-44004-400-44-40000400000000000000000022−2200−222200000000000000000000
χ564-4-44004-400-44-400004000000000000000000−22220022−2200000000000000000000
χ574-4-4400-44004-4-400004000000000000000022−220022−220000000000000000000000
χ584-4-4400-44004-4-4000040000000000000000−222200−22220000000000000000000000
χ594-4-4400-4400-4440000-400000000000000002i2−2i200−2i22i20000000000000000000000
χ604-4-4400-4400-4440000-40000000000000000−2i22i2002i2−2i20000000000000000000000
χ618-88-800008i−8i0000000000000000000000000000000000000000000000000000
χ628-88-80000−8i8i0000000000000000000000000000000000000000000000000000

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