Finite Group Databasebeta

← Group #269608

Character table — Group #269608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111-1-1-1-11111111111-1-11-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-111111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111111111111-1-11-1-1-1-1-1-11
χ17222222222-2-2222-2-200002222-2-2222200000022-2-200-2-20000000000000000-20000000000
χ18222222222-2-2222-2-200002222-2-2-2-2-2-2000000-2-2-2-20022000000000000000020000000000
χ19222222222-2-2222-2-20000-2-2-2-2-2-22222000000-2-22200-2-2000000000000000020000000000
χ20222222222-2-2222-2-20000-2-2-2-2-2-2-2-2-2-2000000222200220000000000000000-20000000000
χ2122222222-222-2-2-22222220000-2-200002222-2-2000022000000-2-20000000000000-20000000
χ2222222222-222-2-2-22222220000-2-20000-2-2-2-2-2-20000-2-200000022000000000000020000000
χ2322222222-222-2-2-222-2-2-2-20000-2-200002222220000-2-2000000-2-2000000000000020000000
χ2422222222-222-2-2-222-2-2-2-20000-2-20000-2-2-2-222000022000000220000000000000-20000000
χ252-222-2-22-202-20002-22i2i−2i−2i000000i2i2−i2−i222-2-20000002i−2ii2−i222−2−2000000i2i2−i2−i2000000002−2000
χ262-222-2-22-202-20002-22i2i−2i−2i000000i2i2−i2−i2-2-222000000−2i2ii2−i222−2−2000000−i2−i2i2i200000000−22000
χ272-222-2-22-202-20002-22i2i−2i−2i000000−i2−i2i2i222-2-20000002i−2i−i2i2−2−222000000−i2−i2i2i200000000−22000
χ282-222-2-22-202-20002-22i2i−2i−2i000000−i2−i2i2i2-2-222000000−2i2i−i2i2−2−222000000i2i2−i2−i2000000002−2000
χ292-222-2-22-202-20002-2−2i−2i2i2i000000i2i2−i2−i222-2-2000000−2i2ii2−i2−2−222000000i2i2−i2−i200000000−22000
χ302-222-2-22-202-20002-2−2i−2i2i2i000000i2i2−i2−i2-2-2220000002i−2ii2−i2−2−222000000−i2−i2i2i2000000002−2000
χ312-222-2-22-202-20002-2−2i−2i2i2i000000−i2−i2i2i222-2-2000000−2i2i−i2i222−2−2000000−i2−i2i2i2000000002−2000
χ322-222-2-22-202-20002-2−2i−2i2i2i000000−i2−i2i2i2-2-2220000002i−2i−i2i222−2−2000000i2i2−i2−i200000000−22000
χ332-22-222-2-2200-2-2200000022-2-2002-22-2i2−i2i2−i2002-20000000000i2−i2i2i2−i2−i2i2−i2i2−i20000000000i2−i20
χ342-22-222-2-2200-2-2200000022-2-2002-22-2−i2i2−i2i2002-20000000000−i2i2−i2−i2i2i2−i2i2−i2i20000000000−i2i20
χ352-22-222-2-2200-2-2200000022-2-200-22-22i2−i2i2−i200-220000000000i2−i2i2i2−i2−i2−i2i2−i2i20000000000−i2i20
χ362-22-222-2-2200-2-2200000022-2-200-22-22−i2i2−i2i200-220000000000−i2i2−i2−i2i2i2i2−i2i2−i20000000000i2−i20
χ372-22-222-2-2200-2-22000000-2-222002-22-2i2−i2i2−i200-220000000000i2−i2−i2−i2i2i2i2−i2i2−i20000000000−i2i20
χ382-22-222-2-2200-2-22000000-2-222002-22-2−i2i2−i2i200-220000000000−i2i2i2i2−i2−i2−i2i2−i2i20000000000i2−i20
χ392-22-222-2-2200-2-22000000-2-22200-22-22i2−i2i2−i2002-20000000000i2−i2−i2−i2i2i2−i2i2−i2i20000000000i2−i20
χ402-22-222-2-2200-2-22000000-2-22200-22-22−i2i2−i2i2002-20000000000−i2i2i2i2−i2−i2i2−i2i2−i20000000000−i2i20
χ412-2-2-2-2222222-22-2-2-200002-22-22-20000000000002-200002i−2i2i−2i00000000000002i−2i00000000
χ422-2-2-2-2222222-22-2-2-200002-22-22-20000000000002-20000−2i2i−2i2i0000000000000−2i2i00000000
χ432-2-2-2-2222222-22-2-2-20000-22-222-2000000000000-2200002i−2i2i−2i0000000000000−2i2i00000000
χ442-2-2-2-2222222-22-2-2-20000-22-222-2000000000000-220000−2i2i−2i2i00000000000002i−2i00000000
χ452-2-2-2-22222-2-2-22-2222-22-22-22-2-22000000002-200-220000000000000000002-200000000000
χ462-2-2-2-22222-2-2-22-2222-22-2-22-22-22000000002-2002-2000000000000000000-2200000000000
χ472-2-2-2-22222-2-2-22-222-22-222-22-2-2200000000-2200-22000000000000000000-2200000000000
χ482-2-2-2-22222-2-2-22-222-22-22-22-22-2200000000-22002-20000000000000000002-200000000000
χ492-2-2-2-2222-2-2-22-22222-22-200002-200000000-22000000000000002-22-200000000002-200000
χ502-2-2-2-2222-2-2-22-22222-22-200002-200000000-2200000000000000-22-220000000000-2200000
χ512-2-2-2-2222-2-2-22-2222-22-2200002-2000000002-2000000000000002-22-20000000000-2200000
χ522-2-2-2-2222-2-2-22-2222-22-2200002-2000000002-200000000000000-22-2200000000002-200000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ55444-4-4-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ56444-4-4-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ57444-4-4-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ5844-44-44-4-44004-4-40000004-4-4400000000000000000000000000000000000000000000000
χ5944-44-44-4-44004-4-4000000-444-400000000000000000000000000000000000000000000000
χ6044-44-44-4-4-400-4440000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6144-44-44-4-4-400-444000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ6244-4-44-44-404-4000-4400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ6344-4-44-44-404-4000-440000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ6444-4-44-44-40-440004-44i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6544-4-44-44-40-440004-4−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ664-444-4-44-40-44000-4400000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ674-444-4-44-40-44000-440000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ684-44-444-4-4-40044-400000000000000002i2−2i22i2−2i200000000000000−2i22i2000000000000000000000
χ694-44-444-4-4-40044-40000000000000000−2i22i2−2i22i2000000000000002i2−2i2000000000000000000000
χ704-4-4-4-4444-4444-44-4-400000000-44000000000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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