Finite Group Databasebeta

← Group #272202

Character table — Group #272202

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444444488882444444888888888822244888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-11-1-1111111111-1-11-1111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1111-1-1-1-1
χ4111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-11111
χ511111111111111111-1-11111111-1-1-111111-1-1111111-1-1-1-11-1-1-1111-1-111-1-1
χ611111111111111111-1-11111111-1-1-1-1-11-1-1-1-1111111-111-1-1-1-1-1-1-1-111-1-111
χ711111111111111111-1-111-1-1-1-11-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ811111111111111111-1-111-1-1-1-11-1-1-1-1-11-1-111-1-1-1-1-1-1-111-1-111111-11111-1-1
χ91111111111111-1-1-1-111111111-111111-1-1-11111-1-1-1-1-111-111-1-111-1-1-1-1-11-1
χ101111111111111-1-1-1-111111111-1111-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-111111-11
χ111111111111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-11111-111-11-111-1-1-1-1-111-11
χ121111111111111-1-1-1-11111-1-1-1-1-1111-1-1-111-1-1-1-11111-1-1-1-1-1-11111111-1-11-1
χ131111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-111-1-1-1-11-1-111-11111-111-1-1-11
χ141111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-11-1-1111-1
χ151111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-111-1-111111-1-1111-1-1-1-1-111111-1
χ161111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-11-1-1111-1-1-1-1-11
χ172222222-22-2-2-22000022-2-200000-2-220000000002i2i−2i−2i0000002i−2i000000000
χ182222222-22-2-2-22000022-2-200000-2-22000000000−2i−2i2i2i000000−2i2i000000000
χ192222222-22-2-2-220000-2-2-2-20000022-20000000002i2i−2i−2i000000−2i2i000000000
χ202222222-22-2-2-220000-2-2-2-20000022-2000000000−2i−2i2i2i0000002i−2i000000000
χ21222222-22-2222-2222200-2-20000-200022-222000000000000-200000-2000000
χ22222222-22-2222-2222200-2-20000-2000-2-2-2-2-20000000000002000002000000
χ23222222-22-2222-2-2-2-2-200-2-200002000222-2-2000000000000-2000002000000
χ24222222-22-2222-2-2-2-2-200-2-200002000-2-2222000000000000200000-2000000
χ252222-2-2222-2-22-222-2-2222-2000022-2-200-20000000000-20020000000000000
χ262222-2-2222-2-22-222-2-2-2-22-200002-22200-20000000000200-20000000000000
χ272222-2-2222-2-22-2-2-222222-20000-22-2-20020000000000200-20000000000000
χ282222-2-2222-2-22-2-2-222-2-22-20000-2-2220020000000000-20020000000000000
χ292222-2-22-2222-2-2000022-2222220-22-20000022-2-2000000000-200000000000
χ302222-2-22-2222-2-2000022-22-2-2-2-20-22-200000-2-222000000000200000000000
χ312222-2-22-2222-2-20000-2-2-22222202-2200000-2-2-2-2000000000200000000000
χ322222-2-22-2222-2-20000-2-2-22-2-2-2-202-22000002222000000000-200000000000
χ332222-2-2-22-2-2-22222-2-200-220000-2000002000000000002-2000000002-20000
χ342222-2-2-22-2-2-22222-2-200-220000-200000200000000000-2200000000-220000
χ352222-2-2-22-2-2-222-2-22200-220000200000-2000000000002-200000000-220000
χ362222-2-2-22-2-2-222-2-22200-220000200000-200000000000-22000000002-20000
χ372-2-222-20202-2-202i−2i2i−2i000022−2−200002i−2i02-2002−2i2−i2i2−i200000000i2−i20002−200
χ382-2-222-20202-2-202i−2i2i−2i000022−2−20000−2i2i0-22002−2i2−i2i2−i200000000−i2i2000−2200
χ392-2-222-20202-2-202i−2i2i−2i0000−2−22200002i−2i02-200−22−i2i2−i2i200000000−i2i2000−2200
χ402-2-222-20202-2-202i−2i2i−2i0000−2−2220000−2i2i0-2200−22−i2i2−i2i200000000i2−i20002−200
χ412-2-222-20202-2-20−2i2i−2i2i000022−2−200002i−2i0-22002−2−i2i2−i2i200000000i2−i2000−2200
χ422-2-222-20202-2-20−2i2i−2i2i000022−2−20000−2i2i02-2002−2−i2i2−i2i200000000−i2i20002−200
χ432-2-222-20202-2-20−2i2i−2i2i0000−2−22200002i−2i0-2200−22i2−i2i2−i200000000−i2i20002−200
χ442-2-222-20202-2-20−2i2i−2i2i0000−2−2220000−2i2i02-200−22i2−i2i2−i200000000i2−i2000−2200
χ45444444-4-4-4-4-4-4-40000004400000000000000000000000000000000000000
χ464444-4-4-4-4-444-440000004-400000000000000000000000000000000000000
χ4744-4-400-404000000004i−4i002i2−2i22i2−2i200000000022−2200000000000000000000000
χ4844-4-400-404000000004i−4i00−2i22i2−2i22i2000000000−222200000000000000000000000
χ4944-4-400-40400000000−4i4i002i2−2i22i2−2i2000000000−222200000000000000000000000
χ5044-4-400-40400000000−4i4i00−2i22i2−2i22i200000000022−2200000000000000000000000
χ514-4-444-40-40-4440000000000000000000000000022−22−222200000000000000000
χ524-4-444-40-40-44400000000000000000000000000−222222−2200000000000000000
χ534-4-44-44040-44-404i−4i−4i4i000000000000000000000000000000000000000000
χ544-4-44-44040-44-40−4i4i4i−4i000000000000000000000000000000000000000000
χ554-4-44-440-404-440000000002222−22−2200000000000−2222000000000000000000000
χ564-4-44-440-404-44000000000−22−2222220000000000022−22000000000000000000000
χ5788-8-80080-800000000000000000000000000000000000000000000000000
χ588-88-8000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ598-88-800000000000000000−4i4i4i−4i0000000000000000000000000000000000

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