Finite Group Databasebeta

← Group #272274

Character table — Group #272274

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444422444444488884444444888888888824444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111-111-1-1-1-1111-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ511111111111111-1-11111111111-11-1-11111-1-11111111-1-1-1-111-1-1-11-1-111-1-1
χ611111111111111-1-11111111111-11-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-1-111
χ711111111111111-1-111111-1-1-1-11-11-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-111
χ811111111111111-1-111111-1-1-1-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111-11111-1-1
χ9111111111111-1-1111-1-1111111-11-11111-1-11111-1-1-1-11-1-111111-1-1-1-1-1-1-11-1
χ10111111111111-1-1111-1-1111111-11-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-111111-11
χ11111111111111-1-1111-1-111-1-1-1-1-11-11111-1-1-1-1-1-111111-1-111-1-1-111-1-1-111-11
χ12111111111111-1-1111-1-111-1-1-1-1-11-111-1-111-1-1-1-11111-1-1-1-1-111-111111-1-11-1
χ13111111111111-1-1-1-11-1-1111111-1-1-1-1-111-1-1-1-111-1-1-1-1111-1-111-111-111-1-1-11
χ14111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-1-11111-1-1-1111-1-1111-1
χ15111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11111111-1-1-1-11-1-1-111111-1
χ16111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-11111111-1-11-1-1-1-1-11
χ172222222-2-22-2-20022200-2-20000020-2-2000000002i2i−2i−2i000000002i−2i0000000
χ182222222-2-22-2-20022200-2-20000020-2-200000000−2i−2i2i2i00000000−2i2i0000000
χ192222222-2-22-2-200-2-2200-2-200000-2022000000002i2i−2i−2i00000000−2i2i0000000
χ202222222-2-22-2-200-2-2200-2-200000-202200000000−2i−2i2i2i000000002i−2i0000000
χ21222222-222-2222200-222-2-20000-20-200222200000000-2000000000-2000000
χ22222222-222-2222200-222-2-20000-20-200-2-2-2-20000000020000000002000000
χ23222222-222-222-2-200-2-2-2-2-200002020022-2-200000000-20000000002000000
χ24222222-222-222-2-200-2-2-2-2-2000020200-2-222000000002000000000-2000000
χ252222-2-222-222-20022-200-2222220-202-2000022-2-200000000000-2000000000
χ262222-2-222-222-20022-200-22-2-2-2-20-202-20000-2-222000000000002000000000
χ272222-2-222-222-200-2-2-200-222222020-220000-2-2-2-2000000000002000000000
χ282222-2-222-222-200-2-2-200-22-2-2-2-2020-220000222200000000000-2000000000
χ292222-2-22-222-222222-2-2-22-20000-2-22-2200000000000002-200000000000000
χ302222-2-22-222-2222-2-2-2-2-22-20000-2222-20000000000000-2200000000000000
χ312222-2-22-222-22-2-222-2222-200002-2-2-220000000000000-2200000000000000
χ322222-2-22-222-22-2-2-2-2-2222-2000022-22-200000000000002-200000000000000
χ332222-2-2-2-22-2-2222002-2-2-22000020-2000000000000000002-20000002-20000
χ342222-2-2-2-22-2-2222002-2-2-22000020-200000000000000000-22000000-220000
χ352222-2-2-2-22-2-22-2-200222-220000-202000000000000000002-2000000-220000
χ362222-2-2-2-22-2-22-2-200222-220000-20200000000000000000-220000002-20000
χ372-2-222-202-20-222-20002-20022−2−2000002i−2i2i−2i002−22−22−200000i2−i2000000i2−i200
χ382-2-222-202-20-222-20002-20022−2−200000−2i2i−2i2i002−22−22−200000−i2i2000000−i2i200
χ392-2-222-202-20-222-20002-200−2−222000002i−2i2i−2i00−22−22−2200000−i2i2000000−i2i200
χ402-2-222-202-20-222-20002-200−2−22200000−2i2i−2i2i00−22−22−2200000i2−i2000000i2−i200
χ412-2-222-202-20-22-22000-220022−2−2000002i−2i−2i2i002−2−22−2200000i2−i2000000−i2i200
χ422-2-222-202-20-22-22000-220022−2−200000−2i2i2i−2i002−2−22−2200000−i2i2000000i2−i200
χ432-2-222-202-20-22-22000-2200−2−222000002i−2i−2i2i00−222−22−200000−i2i2000000i2−i200
χ442-2-222-202-20-22-22000-2200−2−22200000−2i2i2i−2i00−222−22−200000i2−i2000000−i2i200
χ45444444-4-4-4-4-4-40000-4004400000000000000000000000000000000000000
χ464444-4-4-44-4-44-400004004-400000000000000000000000000000000000000
χ474-44-400-400400004i−4i0000022−2222−220000000002i2−2i200000000000000000000000
χ484-44-400-400400004i−4i00000−2222−2222000000000−2i22i200000000000000000000000
χ494-44-400-40040000−4i4i0000022−2222−22000000000−2i22i200000000000000000000000
χ504-44-400-40040000−4i4i00000−2222−22220000000002i2−2i200000000000000000000000
χ514-4-444-40-4404-4000000000000000000000000002i2−2i2−2i22i200000000000000000
χ524-4-444-40-4404-400000000000000000000000000−2i22i22i2−2i200000000000000000
χ534-4-44-440440-4-40000000002222−22−2200000000000−2222000000000000000000000
χ544-4-44-440440-4-4000000000−22−2222220000000000022−22000000000000000000000
χ554-4-44-440-4-40444-4000-440000000000000000000000000000000000000000
χ564-4-44-440-4-4044-440004-40000000000000000000000000000000000000000
χ5788-8-8000000000000000004-4-440000000000000000000000000000000000
χ5888-8-800000000000000000-444-40000000000000000000000000000000000
χ598-88-800800-80000000000000000000000000000000000000000000000000

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