Finite Group Databasebeta

← Group #282721

Character table — Group #282721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ511111111111111111111-1-1-1-11111111111-1-11111-1-111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-11-1-1111111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-111111111-11-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11-11111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ17222222222-2-222-22-200002222-2-222220000-2-2000022-2-2000000000000000-200000000000
χ18222222222-2-222-22-200002222-2-2-2-2-2-20000-2-20000-2-222000000000000000200000000000
χ19222222222-2-222-22-20000-2-2-2-2-2-222220000220000-2-2-2-2000000000000000200000000000
χ20222222222-2-222-22-20000-2-2-2-2-2-2-2-2-2-200002200002222000000000000000-200000000000
χ2122222222-222-2-22-2222220000-2-20000222200-2-2220000-2-2000000000000-2000000000000
χ2222222222-222-2-22-2222220000-2-20000-2-2-2-200-2-2-2-20000220000000000002000000000000
χ2322222222-222-2-22-22-2-2-2-20000-2-2000022220022-2-20000-2-20000000000002000000000000
χ2422222222-222-2-22-22-2-2-2-20000-2-20000-2-2-2-2002222000022000000000000-2000000000000
χ252-2222-2-2-2-2002-202000002i2i−2i−2i0022-2-222−2−20000002i−2i002−20000i2i2−i2−i222−2−20000000000i2−i20
χ262-2222-2-2-2-2002-202000002i2i−2i−2i0022-2-2−2−2220000002i−2i00−220000−i2−i2i2i2−2−2220000000000−i2i20
χ272-2222-2-2-2-2002-202000002i2i−2i−2i00-2-22222−2−2000000−2i2i002−20000i2i2−i2−i2−2−2220000000000−i2i20
χ282-2222-2-2-2-2002-202000002i2i−2i−2i00-2-222−2−222000000−2i2i00−220000−i2−i2i2i222−2−20000000000i2−i20
χ292-2222-2-2-2-2002-20200000−2i−2i2i2i0022-2-222−2−2000000−2i2i002−20000−i2−i2i2i222−2−20000000000−i2i20
χ302-2222-2-2-2-2002-20200000−2i−2i2i2i0022-2-2−2−222000000−2i2i00−220000i2i2−i2−i2−2−2220000000000i2−i20
χ312-2222-2-2-2-2002-20200000−2i−2i2i2i00-2-22222−2−20000002i−2i002−20000−i2−i2i2i2−2−2220000000000i2−i20
χ322-2222-2-2-2-2002-20200000−2i−2i2i2i00-2-222−2−2220000002i−2i00−220000i2i2−i2−i222−2−20000000000−i2i20
χ332-2-22-2-222222-2-2-22-22i2i−2i−2i2-22-22-2000000002-22i−2i00000000000000000000002i−2i000000000
χ342-2-22-2-222222-2-2-22-22i2i−2i−2i-22-222-200000000-222i−2i0000000000000000000000−2i2i000000000
χ352-2-22-2-222222-2-2-22-2−2i−2i2i2i2-22-22-2000000002-2−2i2i0000000000000000000000−2i2i000000000
χ362-2-22-2-222222-2-2-22-2−2i−2i2i2i-22-222-200000000-22−2i2i00000000000000000000002i−2i000000000
χ372-2-22-2-2222-2-2-2-222200002-22-2-2200000000-22000000000022-2-20000000000002-20000000
χ382-2-22-2-2222-2-2-2-222200002-22-2-2200000000-220000000000-2-222000000000000-220000000
χ392-2-22-2-2222-2-2-2-22220000-22-22-22000000002-2000000000022-2-2000000000000-220000000
χ402-2-22-2-2222-2-2-2-22220000-22-22-22000000002-20000000000-2-2220000000000002-20000000
χ412-2-22-2-222-22222-2-2-22i2i−2i−2i0000-220000000000−2i2i0000000000002i−2i2i−2i00000000002-200000
χ422-2-22-2-222-22222-2-2-22i2i−2i−2i0000-220000000000−2i2i000000000000−2i2i−2i2i0000000000-2200000
χ432-2-22-2-222-22222-2-2-2−2i−2i2i2i0000-2200000000002i−2i0000000000002i−2i2i−2i0000000000-2200000
χ442-2-22-2-222-22222-2-2-2−2i−2i2i2i0000-2200000000002i−2i000000000000−2i2i−2i2i00000000002-200000
χ452-2-2-2222-202-20020-22-22-20000002−22−22i−2i2i−2i00002i−2i002−2002−22−20000i2−i2i2−i200000000i2−i2000
χ462-2-2-2222-202-20020-22-22-20000002−22−2−2i2i−2i2i0000−2i2i002−2002−22−20000−i2i2−i2i200000000−i2i2000
χ472-2-2-2222-202-20020-22-22-2000000−22−222i−2i2i−2i00002i−2i00−2200−22−220000−i2i2−i2i200000000−i2i2000
χ482-2-2-2222-202-20020-22-22-2000000−22−22−2i2i−2i2i0000−2i2i00−2200−22−220000i2−i2i2−i200000000i2−i2000
χ492-2-2-2222-202-20020-2-22-220000002−22−22i−2i2i−2i0000−2i2i002−200−22−220000i2−i2i2−i200000000−i2i2000
χ502-2-2-2222-202-20020-2-22-220000002−22−2−2i2i−2i2i00002i−2i002−200−22−220000−i2i2−i2i200000000i2−i2000
χ512-2-2-2222-202-20020-2-22-22000000−22−222i−2i2i−2i0000−2i2i00−22002−22−20000−i2i2−i2i200000000i2−i2000
χ522-2-2-2222-202-20020-2-22-22000000−22−22−2i2i−2i2i00002i−2i00−22002−22−20000i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-404-400-4044i−4i−4i4i000000000000000000000000000000000000000000000000000
χ55444-4-4-44-404-400-404−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ56444-4-4-44-40-440040-400000000000000000000000000000022−22−2222000000000000000000000
χ57444-4-4-44-40-440040-4000000000000000000000000000000−222222−22000000000000000000000
χ5844-44-44-4-44004-40-40000000000000000000000000000000000022−22−222200000000000000000
χ5944-44-44-4-44004-40-400000000000000000000000000000000000−222222−2200000000000000000
χ6044-44-44-4-4-400-4404000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ6144-44-44-4-4-400-440400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ6244-4-44-4-4400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ6344-4-44-4-4400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ6444-4-44-4-44000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ6544-4-44-4-44000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ664-4444-4-4-4400-440-40000000000000002222−22−220000000000−22220000000000000000000000000
χ674-4444-4-4-4400-440-4000000000000000−22−222222000000000022−220000000000000000000000000
χ684-4-44-4-444-4-4-4444-44000000004-4000000000000000000000000000000000000000000000
χ694-4-4-4444-40-4400-404000000000022−2222−22000000000000−2222000000000000000000000000000
χ704-4-4-4444-40-4400-4040000000000−2222−222200000000000022−22000000000000000000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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