Finite Group Databasebeta

← Group #288582

Character table — Group #288582

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888844448888888888888882224448888888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111111-1-11-1-1-1-111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111111-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-111-111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11-1-11-1-11111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ9111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1111111-1-111-1-1-1-111-111-11-1-1-111-1-11-1
χ10111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-11111-1-11111-1-1-1-11-111-11-11-1-1-1-111-11
χ11111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-11-1-11-11-111-1-111-11
χ12111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-11111-1-11-1-11-111111-1-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-1-1-1-1-11-1-111-11111-1-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-111-1-1-1-11111-1-1-1-1-11-1-11-1-1111-1-1111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-111111-111-111-1-1-1-1-1111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1111111-111-1-11-1-111-1-1-11
χ17222222-22222-22222-2-2-2-2-22200000000-200002222000000000000-2-200000000
χ18222222-22222-22222-2-2-2-2-22200000000-20000-2-2-2-20000000000002200000000
χ19222222-22222-2-2-2-2-2-2-2-222-2-2000000002000022-2-2000000000000-2200000000
χ20222222-22222-2-2-2-2-2-2-2-222-2-20000000020000-2-2220000000000002-200000000
χ21222222-2-2-2-2-2-20000-22200002i2i−2i−2i00000002i−2i00000022-2-2000000002i−2i000000
χ22222222-2-2-2-2-2-20000-22200002i2i−2i−2i00000002i−2i000000-2-22200000000−2i2i000000
χ23222222-2-2-2-2-2-20000-2220000−2i−2i2i2i0000000−2i2i00000022-2-200000000−2i2i000000
χ24222222-2-2-2-2-2-20000-2220000−2i−2i2i2i0000000−2i2i000000-2-222000000002i−2i000000
χ252222-2-222-22-222222-2-2222-2-200000000-2000000000000000220-2-20000000000
χ262222-2-222-22-222222-2-2222-2-200000000-2000000000000000-2-20220000000000
χ272222-2-222-22-22-2-2-2-2-2-22-2-2220000000020000000000000002-20-220000000000
χ282222-2-222-22-22-2-2-2-2-2-22-2-222000000002000000000000000-2202-20000000000
χ292222-2-22-22-2220000-22-2000022220000022-2-20000-2-20000200-2000000000000
χ302222-2-22-22-2220000-22-20000222200000-2-2-2-20000220000-2002000000000000
χ312222-2-22-22-2220000-22-20000-2-2-2-20000022220000-2-20000-2002000000000000
χ322222-2-22-22-2220000-22-20000-2-2-2-200000-2-2220000220000200-2000000000000
χ332222-2-2-22-22-2-2222222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i200−2i2i00000000000000000000000000
χ342222-2-2-22-22-2-2222222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i2002i−2i00000000000000000000000000
χ352222-2-2-22-22-2-2-2-2-2-222-222222i2i−2i−2i−2i−2i2i2i-200−2i2i00000000000000000000000000
χ362222-2-2-22-22-2-2-2-2-2-222-22222−2i−2i2i2i2i2i−2i−2i-2002i−2i00000000000000000000000000
χ372-22-22-20-222-2022-2-2000002-2000000000i2−i2002i−2i2i−2ii2−i2i2−i2i2−i200000000002−22−200
χ382-22-22-20-222-2022-2-2000002-2000000000i2−i200−2i2i−2i2ii2−i2i2−i2i2−i20000000000−22−2200
χ392-22-22-20-222-2022-2-2000002-2000000000−i2i2002i−2i2i−2i−i2i2−i2i2−i2i20000000000−22−2200
χ402-22-22-20-222-2022-2-2000002-2000000000−i2i200−2i2i−2i2i−i2i2−i2i2−i2i200000000002−22−200
χ412-22-22-20-222-20-2-22200000-22000000000i2−i2002i−2i−2i2ii2−i2−i2i2−i2i200000000002−2−2200
χ422-22-22-20-222-20-2-22200000-22000000000i2−i200−2i2i2i−2ii2−i2−i2i2−i2i20000000000−222−200
χ432-22-22-20-222-20-2-22200000-22000000000−i2i2002i−2i−2i2i−i2i2i2−i2i2−i20000000000−222−200
χ442-22-22-20-222-20-2-22200000-22000000000−i2i200−2i2i2i−2i−i2i2i2−i2i2−i200000000002−2−2200
χ454444444-4-4-4-4400004-4-40000000000000000000000000000000000000000000
χ464444-4-4-4-44-44-400004-440000000000000000000000000000000000000000000
χ4744-4-40040000-422−2222−2200022−220022−2222−222-22-20000000000000000000000000000000
χ4844-4-40040000-422−2222−2200022−2200−2222−2222-22-220000000000000000000000000000000
χ4944-4-40040000-4−2222−2222000−22220022−2222−22-22-220000000000000000000000000000000
χ5044-4-40040000-4−2222−2222000−222200−2222−22222-22-20000000000000000000000000000000
χ5144-4-400-40000422−2222−22000−2222002i2−2i2−2i22i22i−2i−2i2i0000000000000000000000000000000
χ5244-4-400-40000422−2222−22000−222200−2i22i22i2−2i2−2i2i2i−2i0000000000000000000000000000000
χ5344-4-400-400004−2222−222200022−22002i2−2i2−2i22i2−2i2i2i−2i0000000000000000000000000000000
χ5444-4-400-400004−2222−222200022−2200−2i22i22i2−2i22i−2i−2i2i0000000000000000000000000000000
χ554-44-44-404-4-4400000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ564-44-44-404-4-440000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ574-44-4-44044-4-40000000000000000000002i2−2i2000000−2i22i200000000000000000000
χ584-44-4-44044-4-4000000000000000000000−2i22i20000002i2−2i200000000000000000000
χ594-44-4-440-4-444044-4-400000-44000000000000000000000000000000000000000
χ604-44-4-440-4-4440-4-444000004-4000000000000000000000000000000000000000
χ618-8-880000000042−42−42420000000000000000000000000000000000000000000000
χ628-8-8800000000−424242−420000000000000000000000000000000000000000000000

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