Finite Group Databasebeta

← Group #272189

Character table — Group #272189

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444422444444488882222444888888888824444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1111-1-1111111111-11-1-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-11111
χ511111111111111111-1-1111111-1-11111-111-1-1111111-11-1-1-1111-1-1-1-1-111-1-1
χ611111111111111111-1-1111111-1-1-1-111-1-1-1-1-1111111-1-1-111-1-1-111-1-1-1-1-111
χ711111111111111111-1-111-1-1-1-1-1-11111-11111-1-1-1-1-1-1-11-1-1-1-1-11-1-1111-1-111
χ811111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-11111-11111111-1-1
χ9111111111111-1-11-1-1111111111111-1-11-1-11111-1-1-1-1-11-11111-1-1-11-1-1-1-11-1
χ10111111111111-1-11-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-11
χ11111111111111-1-11-1-11111-1-1-1-11111-1-11-1-1-1-1-1-11111-11-111-1-1-1-1-1-11111-11
χ12111111111111-1-11-1-11111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-111111-111-1-11-1
χ13111111111111-1-11-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-1-1-1111-1-111-111-111-1-1-11
χ14111111111111-1-11-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-11-1111-1-11-1-1-111111-1
χ15111111111111-1-11-1-1-1-111-1-1-1-1-1-111-1-1-1-1-111-1-11111111-1-1-1-1-1111-1-1111-1
χ16111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1111111-1-11-1-1-1-1-11
χ172222222-22-2-2-20020022-2-20000-2-2000020000002i2i−2i−2i000000000002i−2i0000
χ182222222-22-2-2-20020022-2-20000-2-200002000000−2i−2i2i2i00000000000−2i2i0000
χ192222222-22-2-2-200200-2-2-2-20000220000-20000002i2i−2i−2i00000000000−2i2i0000
χ202222222-22-2-2-200200-2-2-2-20000220000-2000000−2i−2i2i2i000000000002i−2i0000
χ21222222-22-222222-22200-2-200000022-2-2022000000000-200000-2000000000
χ22222222-22-222222-22200-2-2000000-2-2-2-20-2-20000000002000002000000000
χ23222222-22-2222-2-2-2-2-200-2-200000022220-2-2000000000-2000002000000000
χ24222222-22-2222-2-2-2-2-200-2-2000000-2-222022000000000200000-2000000000
χ252222-2-2222-2-2200-20022-2222222-20000-20022-2-200000000000000-2000000
χ262222-2-2222-2-2200-20022-22-2-2-2-22-20000-200-2-222000000000000002000000
χ272222-2-2222-2-2200-200-2-2-222222-220000200-2-2-2-2000000000000002000000
χ282222-2-2222-2-2200-200-2-2-22-2-2-2-2-220000200222200000000000000-2000000
χ292222-2-22-2222-222-2-2-2222-20000-2200-22-20000000000-20200000000000000
χ302222-2-22-2222-222-2-2-2-2-22-200002-200-222000000000020-200000000000000
χ312222-2-22-2222-2-2-2-222222-20000-22002-2-2000000000020-200000000000000
χ322222-2-22-2222-2-2-2-222-2-22-200002-2002-220000000000-20200000000000000
χ332222-2-2-2-2-222-2222-2-200-22000000002-2000000000000002-20002-20000000
χ342222-2-2-2-2-222-2222-2-200-22000000002-200000000000000-22000-220000000
χ352222-2-2-2-2-222-2-2-222200-2200000000-22000000000000002-2000-220000000
χ362222-2-2-2-2-222-2-2-222200-2200000000-2200000000000000-220002-20000000
χ372-2-222-20202-2-22-202-20000i2i2−i2−i2002-20002-200i2−i2i2−i2i2−i200000i2−i2000000i2−i200
χ382-2-222-20202-2-22-202-20000i2i2−i2−i200-22000-2200i2−i2i2−i2i2−i200000−i2i2000000−i2i200
χ392-2-222-20202-2-22-202-20000−i2−i2i2i2002-20002-200−i2i2−i2i2−i2i200000−i2i2000000−i2i200
χ402-2-222-20202-2-22-202-20000−i2−i2i2i200-22000-2200−i2i2−i2i2−i2i200000i2−i2000000i2−i200
χ412-2-222-20202-2-2-220-220000i2i2−i2−i2002-2000-2200i2−i2−i2i2−i2i200000i2−i2000000−i2i200
χ422-2-222-20202-2-2-220-220000i2i2−i2−i200-220002-200i2−i2−i2i2−i2i200000−i2i2000000i2−i200
χ432-2-222-20202-2-2-220-220000−i2−i2i2i2002-2000-2200−i2i2i2−i2i2−i200000−i2i2000000i2−i200
χ442-2-222-20202-2-2-220-220000−i2−i2i2i200-220002-200−i2i2i2−i2i2−i200000i2−i2000000−i2i200
χ45444444-4-4-4-4-4-400-400004400000000000000000000000000000000000000
χ464444-4-4-44-4-4-4400400004-400000000000000000000000000000000000000
χ474-44-40040-4000000004i−4i002i2−2i22i2−2i200000000022−2200000000000000000000000
χ484-44-40040-4000000004i−4i00−2i22i2−2i22i2000000000−222200000000000000000000000
χ494-44-40040-400000000−4i4i002i2−2i22i2−2i2000000000−222200000000000000000000000
χ504-44-40040-400000000−4i4i00−2i22i2−2i22i200000000022−2200000000000000000000000
χ514-4-444-40-40-4440000000000000000000000000022−22−222200000000000000000
χ524-4-444-40-40-44400000000000000000000000000−222222−2200000000000000000
χ534-4-44-44040-44-40000000002i22i2−2i2−2i200000000000−2i22i2000000000000000000000
χ544-4-44-44040-44-4000000000−2i2−2i22i22i2000000000002i2−2i2000000000000000000000
χ554-4-44-440-404-444-40-44000000000000000000000000000000000000000000
χ564-4-44-440-404-44-4404-4000000000000000000000000000000000000000000
χ5788-8-8000000000000000004-4-440000000000000000000000000000000000
χ5888-8-800000000000000000-444-40000000000000000000000000000000000
χ598-88-800-80800000000000000000000000000000000000000000000000000

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