Finite Group Databasebeta

← Group #272205

Character table — Group #272205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444444488882222244888888888844444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-11111111-1-11-1111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-11111
χ511111111111111-1-11111111111-1-1111-1-1-111111111-1-1-1-11-1-1-1111-1-111-1-1
χ611111111111111-1-11111111111-1-1-1-11-1-1-1-1-1111111-111-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-111111-1-1-1-11-1-1111-11111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ811111111111111-1-111111-1-1-1-11-1-1-1-11-111-1-1-1-1-1-1-1-1-111-1-111111-11111-1-1
χ9111111111111-1-1111-1-1111111-11111-1111-1-111-1-1-1-1-111-111-1-111-1-1-1-1-11-1
χ10111111111111-1-1111-1-1111111-111-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-11
χ11111111111111-1-1111-1-111-1-1-1-1-11111-11-1-1-1-1-1-11111-111-11-111-1-1-1-1-111-11
χ12111111111111-1-1111-1-111-1-1-1-1-111-1-1-11-1-111-1-11111-1-1-1-1-1-11111111-1-11-1
χ13111111111111-1-1-1-11-1-1111111-1-1-111-1-1-1-1-1-111-1-1-1-11-1-111-11111-111-1-1-11
χ14111111111111-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-1111-1
χ15111111111111-1-1-1-11-1-111-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-1111-1-1-1-1-111111-1
χ16111111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-11-1-1111-1-1-1-1-11
χ172222222-2-22-2-20022200-2-200000-2-200020000002i2i−2i−2i0000002i−2i000000000
χ182222222-2-22-2-20022200-2-200000-2-20002000000−2i−2i2i2i000000−2i2i000000000
χ192222222-2-22-2-200-2-2200-2-20000022000-20000002i2i−2i−2i000000−2i2i000000000
χ202222222-2-22-2-200-2-2200-2-20000022000-2000000−2i−2i2i2i0000002i−2i000000000
χ21222222-222-2222200-222-2-20000-20022-2000220000000000-200000-2000000
χ22222222-222-2222200-222-2-20000-200-2-2-2000-2-200000000002000002000000
χ23222222-222-222-2-200-2-2-2-2-20000200222000-2-20000000000-2000002000000
χ24222222-222-222-2-200-2-2-2-2-20000200-2-22000220000000000200000-2000000
χ252222-2-22222-2-20022-200-22222202-2000-22200-2-2000000000-200000000000
χ262222-2-22222-2-20022-200-22-2-2-2-202-2000-2-2-20022000000000200000000000
χ272222-2-22222-2-200-2-2-200-2222220-220002-2-200-2-2000000000200000000000
χ282222-2-22222-2-200-2-2-200-22-2-2-2-20-220002220022000000000-200000000000
χ292222-2-22-2-22222222-2-2-22-20000-2-22002-20000000000-20020000000000000
χ302222-2-22-2-222222-2-2-2-2-22-20000-22-200220000000000200-20000000000000
χ312222-2-22-2-2222-2-222-2222-200002-2200-2-20000000000200-20000000000000
χ322222-2-22-2-2222-2-2-2-2-2222-2000022-200-220000000000-20020000000000000
χ332222-2-2-2-2-2-22222002-2-2-22000020000-20000000000002-2000000002-20000
χ342222-2-2-2-2-2-22222002-2-2-22000020000-2000000000000-2200000000-220000
χ352222-2-2-2-2-2-222-2-200222-220000-2000020000000000002-200000000-220000
χ362222-2-2-2-2-2-222-2-200222-220000-200002000000000000-22000000002-20000
χ372-22-22-202-202-22i−2i0002i−2i00i2i2−i2−i20002-200002i−2ii2−i22−22−200000000i2−i20002−200
χ382-22-22-202-202-22i−2i0002i−2i00i2i2−i2−i2000-220000−2i2ii2−i22−22−200000000−i2i2000−2200
χ392-22-22-202-202-22i−2i0002i−2i00−i2−i2i2i20002-200002i−2i−i2i2−22−2200000000−i2i2000−2200
χ402-22-22-202-202-22i−2i0002i−2i00−i2−i2i2i2000-220000−2i2i−i2i2−22−2200000000i2−i20002−200
χ412-22-22-202-202-2−2i2i000−2i2i00i2i2−i2−i20002-20000−2i2ii2−i2−22−2200000000i2−i2000−2200
χ422-22-22-202-202-2−2i2i000−2i2i00i2i2−i2−i2000-2200002i−2ii2−i2−22−2200000000−i2i20002−200
χ432-22-22-202-202-2−2i2i000−2i2i00−i2−i2i2i20002-20000−2i2i−i2i22−22−200000000−i2i20002−200
χ442-22-22-202-202-2−2i2i000−2i2i00−i2−i2i2i2000-2200002i−2i−i2i22−22−200000000i2−i2000−2200
χ45444444-4-4-4-4-4-40000-4004400000000000000000000000000000000000000
χ464444-4-4-444-4-4-400004004-400000000000000000000000000000000000000
χ474-44-44-40-440-44000000000000000000000000002i2−2i2−2i22i200000000000000000
χ484-44-44-40-440-4400000000000000000000000000−2i22i22i2−2i200000000000000000
χ494-44-4-4404-40-440000000002i22i2−2i2−2i200000000000−2i22i2000000000000000000000
χ504-44-4-4404-40-44000000000−2i2−2i22i22i2000000000002i2−2i2000000000000000000000
χ514-44-4-440-4404-44i−4i000−4i4i0000000000000000000000000000000000000000
χ524-44-4-440-4404-4−4i4i0004i−4i0000000000000000000000000000000000000000
χ534-4-4400400-400004i−4i000002i2−2i22i2−2i2000000022−220000000000000000000000000
χ544-4-4400400-400004i−4i00000−2i22i2−2i22i20000000−22220000000000000000000000000
χ554-4-4400400-40000−4i4i000002i2−2i22i2−2i20000000−22220000000000000000000000000
χ564-4-4400400-40000−4i4i00000−2i22i2−2i22i2000000022−220000000000000000000000000
χ5788-8-8000000000000000004-4-440000000000000000000000000000000000
χ5888-8-800000000000000000-444-40000000000000000000000000000000000
χ598-8-8800-80080000000000000000000000000000000000000000000000000

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