Finite Group Databasebeta

← Group #288584

Character table — Group #288584

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888844448888888888888882244448888888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1111111-1-11-1-11-1-111-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11111111-1-1-1-1-1-111-111-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ9111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-11111-1-111-1-1-1-11-111-111-1-1-111-1-11-1
χ10111111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-111-1-11111-1-1-1-1-111-111-11-1-1-1-111-11
χ11111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-11-111-1-111-11
χ12111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-111-1-111-1-11111-11-1-11-1-111111-1-11-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-111-1-111-1-1-1-1-11-1-11-11-11111-1-1-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11-1-11-1-1-1111-1-1111-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111-111-1111-1-1-1-1-1111-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-111111-111-11-11-1-111-1-1-11
χ172222222-2222-22222-2-2-222-2-20000000000-2002222000000000000-2-200000000
χ182222222-2222-22222-2-2-222-2-20000000000-200-2-2-2-20000000000002200000000
χ192222222-2222-2-2-2-2-2-2-2-2-2-222000000000020022-2-2000000000000-2200000000
χ202222222-2222-2-2-2-2-2-2-2-2-2-2220000000000200-2-2220000000000002-200000000
χ21222222-2-2-2-2-2-200002-2200002i2i−2i−2i00000002i−2i00000022-2-2000000002i−2i000000
χ22222222-2-2-2-2-2-200002-2200002i2i−2i−2i00000002i−2i000000-2-22200000000−2i2i000000
χ23222222-2-2-2-2-2-200002-220000−2i−2i2i2i0000000−2i2i00000022-2-200000000−2i2i000000
χ24222222-2-2-2-2-2-200002-220000−2i−2i2i2i0000000−2i2i000000-2-222000000002i−2i000000
χ252222-2-222-22-222222-2-22-2-2220000000000-2000000000000220-2-200000000000
χ262222-2-222-22-222222-2-22-2-2220000000000-2000000000000-2-202200000000000
χ272222-2-222-22-22-2-2-2-2-2-2222-2-2000000000020000000000002-20-2200000000000
χ282222-2-222-22-22-2-2-2-2-2-2222-2-200000000002000000000000-2202-200000000000
χ292222-2-22-2-22-2-2222222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i002−2i2i00000000000000000000000000
χ302222-2-22-2-22-2-2222222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i0022i−2i00000000000000000000000000
χ312222-2-22-2-22-2-2-2-2-2-222-222222i2i−2i−2i−2i−2i2i2i00-2−2i2i00000000000000000000000000
χ322222-2-22-2-22-2-2-2-2-2-222-22222−2i−2i2i2i2i2i−2i−2i00-22i−2i00000000000000000000000000
χ332222-2-2-222-22200002-2-2000022220000220-2-20000-2-2000000200-20000000000
χ342222-2-2-222-22200002-2-2000022220000-2-20-2-2000022000000-20020000000000
χ352222-2-2-222-22200002-2-20000-2-2-2-20000220220000-2-2000000-20020000000000
χ362222-2-2-222-22200002-2-20000-2-2-2-20000-2-2022000022000000200-20000000000
χ372-22-2-2220-2-22022-2-20002-20000000000i2−i20002-22-2i2−i2i2−i2i2−i20000000000i2−i2i2−i200
χ382-22-2-2220-2-22022-2-20002-20000000000i2−i2000-22-22i2−i2i2−i2i2−i20000000000−i2i2−i2i200
χ392-22-2-2220-2-22022-2-20002-20000000000−i2i20002-22-2−i2i2−i2i2−i2i20000000000−i2i2−i2i200
χ402-22-2-2220-2-22022-2-20002-20000000000−i2i2000-22-22−i2i2−i2i2−i2i20000000000i2−i2i2−i200
χ412-22-2-2220-2-220-2-222000-220000000000i2−i20002-2-22i2−i2−i2i2−i2i20000000000i2−i2−i2i200
χ422-22-2-2220-2-220-2-222000-220000000000i2−i2000-222-2i2−i2−i2i2−i2i20000000000−i2i2i2−i200
χ432-22-2-2220-2-220-2-222000-220000000000−i2i20002-2-22−i2i2i2−i2i2−i20000000000−i2i2i2−i200
χ442-22-2-2220-2-220-2-222000-220000000000−i2i2000-222-2−i2i2i2−i2i2−i20000000000i2−i2−i2i200
χ45444444-44-4-4-440000-44-40000000000000000000000000000000000000000000
χ464444-4-4-4-44-44-40000-4440000000000000000000000000000000000000000000
χ474-44-44-4404-4-4044-4-4000-4400000000000000000000000000000000000000000
χ484-44-44-4404-4-40-4-4440004-400000000000000000000000000000000000000000
χ494-44-44-4-40-444000000000000000000002i2−2i20000000−2i22i200000000000000000000
χ504-44-44-4-40-44400000000000000000000−2i22i200000002i2−2i200000000000000000000
χ514-44-4-44-4044-400000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ524-44-4-44-4044-40000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ534-4-440004000-422−2222−220000022−222i2−2i22i2−2i22i−2i2i−2i0000000000000000000000000000000
χ544-4-440004000-422−2222−220000022−22−2i22i2−2i22i2−2i2i−2i2i0000000000000000000000000000000
χ554-4-440004000-4−2222−222200000−22222i2−2i22i2−2i2−2i2i−2i2i0000000000000000000000000000000
χ564-4-440004000-4−2222−222200000−2222−2i22i2−2i22i22i−2i2i−2i0000000000000000000000000000000
χ574-4-44000-4000422−2222−2200000−222222−22−22222-2-220000000000000000000000000000000
χ584-4-44000-4000422−2222−2200000−2222−222222−22-222-20000000000000000000000000000000
χ594-4-44000-40004−2222−22220000022−2222−22−2222-222-20000000000000000000000000000000
χ604-4-44000-40004−2222−22220000022−22−222222−222-2-220000000000000000000000000000000
χ6188-8-80000000042−42−42420000000000000000000000000000000000000000000000
χ6288-8-800000000−424242−420000000000000000000000000000000000000000000000

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