Finite Group Databasebeta

← Group #118367

Character table — Group #118367

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444888888888888888844448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ911111111-1-1-1-1-1-1-1-1-1-11-1-111-111iiii−i−i−i−i1111-1-1-1-111-1-1i−iii−i−iii−i−ii−i11-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-11-1-111-111iiii−i−i−i−i1111-1-1-1-1-1-111−iiii−i−i−i−iii−ii-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-11-1-111-111iiii−i−i−i−i-1-1-1-1111111-1-1−ii−i−iiiii−i−i−ii-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-11-1-111-111iiii−i−i−i−i-1-1-1-11111-1-111i−i−i−iii−i−iiii−i11-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-11-1-111-111−i−i−i−iiiii1111-1-1-1-111-1-1−ii−i−iii−i−iii−ii11-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-11-1-111-111−i−i−i−iiiii1111-1-1-1-1-1-111i−i−i−iiiii−i−ii−i-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-11-1-111-111−i−i−i−iiiii-1-1-1-1111111-1-1i−iii−i−i−i−iiii−i-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-11-1-111-111−i−i−i−iiiii-1-1-1-11111-1-111−iiii−i−iii−i−i−ii11-1-1
χ172222222222-2-2-2-22-2-22222-2-2-2-2-2000000000000000000000000000000002i−2i2i−2i
χ182222222222-2-2-2-22-2-22222-2-2-2-2-200000000000000000000000000000000−2i2i−2i2i
χ1922222222-2-22222-222-22-2-2-2-22-2-2000000000000000000000000000000002i−2i−2i2i
χ2022222222-2-22222-222-22-2-2-2-22-2-200000000000000000000000000000000−2i2i2i−2i
χ21222222-2-222222-222-22-2-2-22-2-22-2000000000000000000002200000000-2-20000
χ22222222-2-222222-222-22-2-2-22-2-22-200000000000000000000-2-200000000220000
χ23222222-2-222-2-2-222-222-2-2-2-222-2222-2-222-2-20000000000000000000000000000
χ24222222-2-222-2-2-222-222-2-2-2-222-22-2-222-2-2220000000000000000000000000000
χ25222222-2-2-2-2222-2-22-2-2-222-22-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ26222222-2-2-2-2222-2-22-2-2-222-22-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ27222222-2-2-2-2-2-2-22-2-22-2-2222-222-2000000000000000000002i−2i00000000−2i2i0000
χ28222222-2-2-2-2-2-2-22-2-22-2-2222-222-200000000000000000000−2i2i000000002i−2i0000
χ292222-2-2222222-2-2-2-2-2-2-22-2222-2-200000000000000002-22-20000000000000000
χ302222-2-2222222-2-2-2-2-2-2-22-2222-2-20000000000000000-22-220000000000000000
χ312222-2-22222-2-222-222-2-22-2-2-2-2220000000022-2-222-2-200000000000000000000
χ322222-2-22222-2-222-222-2-22-2-2-2-22200000000-2-222-2-22200000000000000000000
χ332222-2-222-2-222-2-22-2-22-2-22-2-22220000000022-2-2-2-22200000000000000000000
χ342222-2-222-2-222-2-22-2-22-2-22-2-222200000000-2-22222-2-200000000000000000000
χ352222-2-222-2-2-2-2222222-2-2222-2-2-200000000000000002-2-220000000000000000
χ362222-2-222-2-2-2-2222222-2-2222-2-2-20000000000000000-222-20000000000000000
χ372222-2-2-2-22222-22-2-22-22-222-2-2-2200000000000000000000002i−2i2i−2i0000000000
χ382222-2-2-2-22222-22-2-22-22-222-2-2-220000000000000000000000−2i2i−2i2i0000000000
χ392222-2-2-2-222-2-22-2-22-2-22-22-2222-2000000000000000000000000002i−2i2i−2i000000
χ402222-2-2-2-222-2-22-2-22-2-22-22-2222-200000000000000000000000000−2i2i−2i2i000000
χ412222-2-2-2-2-2-222-222-22222-2-22-22-2000000000000000000000000002-2-22000000
χ422222-2-2-2-2-2-222-222-22222-2-22-22-200000000000000000000000000-222-2000000
χ432222-2-2-2-2-2-2-2-22-222-2222-22-22-2200000000000000000000002-2-220000000000
χ442222-2-2-2-2-2-2-2-22-222-2222-22-22-220000000000000000000000-222-20000000000
χ4544-4-44-4004-40000400-4000000000022−220022−220000000000000000000000000000
χ4644-4-44-4004-40000400-40000000000−222200−22220000000000000000000000000000
χ4744-4-44-400-440000-400400000000002i2−2i200−2i22i20000000000000000000000000000
χ4844-4-44-400-440000-40040000000000−2i22i2002i2−2i20000000000000000000000000000
χ4944-4-4-44004-40000-4004000000002i2−2i2002i2−2i2000000000000000000000000000000
χ5044-4-4-44004-40000-400400000000−2i22i200−2i22i2000000000000000000000000000000
χ5144-4-4-4400-440000400-40000000022−2200−2222000000000000000000000000000000
χ5244-4-4-4400-440000400-400000000−22220022−22000000000000000000000000000000
χ534-44-4004-40000440-4-4000000000000000000022−220022−2200000000000000000000
χ544-44-4004-40000440-4-40000000000000000000−222200−222200000000000000000000
χ554-44-4004-40000-4-4044000000000000000000022−2200−222200000000000000000000
χ564-44-4004-40000-4-40440000000000000000000−22220022−2200000000000000000000
χ574-44-400-4400004-40-44000000000000000002i2−2i2002i2−2i20000000000000000000000
χ584-44-400-4400004-40-4400000000000000000−2i22i200−2i22i20000000000000000000000
χ594-44-400-440000-4404-4000000000000000002i2−2i200−2i22i20000000000000000000000
χ604-44-400-440000-4404-400000000000000000−2i22i2002i2−2i20000000000000000000000
χ618-8-880000008i−8i00000000000000000000000000000000000000000000000000
χ628-8-88000000−8i8i00000000000000000000000000000000000000000000000000

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