Finite Group Databasebeta

← Group #112415

Character table — Group #112415

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444444444448888888822444444888888888888
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111-1-1-111-1-1-1-111-1-1111-11-1-1iiii−i−i−i−i1111-1-1-1-11-11-111-1-1ii−i−iii−i−iii−i−i
χ10111111-1-1-111-1-1-1-111-1-1111-11-1-1iiii−i−i−i−i1111-1-1-1-1-11-11-1-111ii−i−i−i−iii−i−iii
χ11111111-1-1-111-1-1-1-111-1-1111-11-1-1iiii−i−i−i−i-1-1-1-111111-11-1-1-111−i−iii−i−iiiii−i−i
χ12111111-1-1-111-1-1-1-111-1-1111-11-1-1iiii−i−i−i−i-1-1-1-11111-11-1111-1-1−i−iiiii−i−i−i−iii
χ13111111-1-1-111-1-1-1-111-1-1111-11-1-1−i−i−i−iiiii1111-1-1-1-11-11-111-1-1−i−iii−i−iii−i−iii
χ14111111-1-1-111-1-1-1-111-1-1111-11-1-1−i−i−i−iiiii1111-1-1-1-1-11-11-1-111−i−iiiii−i−iii−i−i
χ15111111-1-1-111-1-1-1-111-1-1111-11-1-1−i−i−i−iiiii-1-1-1-111111-11-1-1-111ii−i−iii−i−i−i−iii
χ16111111-1-1-111-1-1-1-111-1-1111-11-1-1−i−i−i−iiiii-1-1-1-11111-11-1111-1-1ii−i−i−i−iiiii−i−i
χ17222222222-2-2-2-222-2-22222-2-2-2-2-200000000000000000000000000002-22-20000
χ18222222222-2-2-2-222-2-22222-2-2-2-2-20000000000000000000000000000-22-220000
χ1922222222-22222-2-2-2-2-22-2-222-2-2-20000000000000000000000002i−2i2i−2i00000000
χ2022222222-22222-2-2-2-2-22-2-222-2-2-2000000000000000000000000−2i2i−2i2i00000000
χ2122222222-2-2-2-2-2-2-222-22-2-2-2-222200000000000000002-2-220000000000000000
χ2222222222-2-2-2-2-2-2-222-22-2-2-2-22220000000000000000-222-20000000000000000
χ23222222-2-2222-2-222-2-22-2-2-22-2-2220000000000000000000000002-2-2200000000
χ24222222-2-2222-2-222-2-22-2-2-22-2-222000000000000000000000000-222-200000000
χ25222222-2-22-2-22222222-2-2-2-222-2-2000000000000000022-2-20000000000000000
χ26222222-2-22-2-22222222-2-2-2-222-2-20000000000000000-2-2220000000000000000
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
χ292222-2-22222222-2-2-2-22-22-2-2-22-2222-2-222-2-20000000000000000000000000000
χ302222-2-22222222-2-2-2-22-22-2-2-22-22-2-222-2-2220000000000000000000000000000
χ312222-2-2222-2-2-2-2-2-2222-22-222-22-2000000000000000000002-22-2000000000000
χ322222-2-2222-2-2-2-2-2-2222-22-222-22-200000000000000000000-22-22000000000000
χ332222-2-222-222222222-2-2-22-2-2-22-20000000022-2-222-2-200000000000000000000
χ342222-2-222-222222222-2-2-22-2-2-22-200000000-2-222-2-22200000000000000000000
χ352222-2-222-2-2-2-2-222-2-2-2-2-22222-22000000000000000000000000000000002-22-2
χ362222-2-222-2-2-2-2-222-2-2-2-2-22222-2200000000000000000000000000000000-22-22
χ372222-2-2-2-2222-2-2-2-22222-22-22-2-220000000022-2-2-2-22200000000000000000000
χ382222-2-2-2-2222-2-2-2-22222-22-22-2-2200000000-2-22222-2-200000000000000000000
χ392222-2-2-2-22-2-222-2-2-2-222-222-222-2000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2-22-2-222-2-2-2-222-222-222-200000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2-2-222-2-222-2-2-222-2-2222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ422222-2-2-2-2-222-2-222-2-2-222-2-2222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ432222-2-2-2-2-2-2-2222222-222-22-2-2-22000000000000000000002-2-22000000000000
χ442222-2-2-2-2-2-2-2222222-222-22-2-2-2200000000000000000000-222-2000000000000
χ4544-4-44-400400004-400-4000000002-22-22-22-20000000000000000000000000000
χ4644-4-44-400400004-400-400000000-22-22-22-220000000000000000000000000000
χ4744-4-44-400-40000-44004000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ4844-4-44-400-40000-4400400000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ4944-4-4-440040000-4400-4000000002-2-222-2-220000000000000000000000000000
χ5044-4-4-440040000-4400-400000000-222-2-222-20000000000000000000000000000
χ5144-4-4-4400-400004-4004000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ5244-4-4-4400-400004-400400000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ534-44-4004-404-44-4000000000000000000000002i2−2i2002i2−2i200000000000000000000
χ544-44-4004-404-44-400000000000000000000000−2i22i200−2i22i200000000000000000000
χ554-44-4004-40-44-440000000000000000000002i2−2i2002i2−2i20000000000000000000000
χ564-44-4004-40-44-44000000000000000000000−2i22i200−2i22i20000000000000000000000
χ574-44-400-4404-4-44000000000000000000000002i2−2i200−2i22i200000000000000000000
χ584-44-400-4404-4-4400000000000000000000000−2i22i2002i2−2i200000000000000000000
χ594-44-400-440-444-40000000000000000000002i2−2i200−2i22i20000000000000000000000
χ604-44-400-440-444-4000000000000000000000−2i22i2002i2−2i20000000000000000000000
χ618-8-88000000000008-8000000000000000000000000000000000000000000000
χ628-8-8800000000000-88000000000000000000000000000000000000000000000

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