Finite Group Databasebeta

← Group #269657

Character table — Group #269657

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-1111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111-1-11-1-111-1-1-1-11
χ172222222222-22-2-2-2200002222-2-20000222200-2-2002200-2-2000000000000000-2000000000
χ182222222222-22-2-2-2200002222-2-20000-2-2-2-200-2-200-2-200220000000000000002000000000
χ192222222222-22-2-2-220000-2-2-2-2-2-200002222002200-2-200-2-20000000000000002000000000
χ202222222222-22-2-2-220000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000000-2000000000
χ2122222222-2-22-2222-222220000-2-222220000-2-2002200-2-200000000000000-2000000000000
χ2222222222-2-22-2222-222220000-2-2-2-2-2-20000-2-200-2-20022000000000000002000000000000
χ2322222222-2-22-2222-2-2-2-2-20000-2-2222200002200-2-200-2-2000000000000002000000000000
χ2422222222-2-22-2222-2-2-2-2-20000-2-2-2-2-2-20000220022002200000000000000-2000000000000
χ252-222-22-2-22-20-2000200002i2i−2i−2i0022−2−222-2-20000002i−2i2−200i2i2−i2−i2000022−2−200000000i2−i2000
χ262-222-22-2-22-20-2000200002i2i−2i−2i0022−2−2-2-222000000−2i2i2−200i2i2−i2−i20000−2−22200000000−i2i2000
χ272-222-22-2-22-20-2000200002i2i−2i−2i00−2−22222-2-20000002i−2i−2200−i2−i2i2i20000−2−22200000000−i2i2000
χ282-222-22-2-22-20-2000200002i2i−2i−2i00−2−222-2-222000000−2i2i−2200−i2−i2i2i2000022−2−200000000i2−i2000
χ292-222-22-2-22-20-200020000−2i−2i2i2i0022−2−222-2-2000000−2i2i2−200−i2−i2i2i2000022−2−200000000−i2i2000
χ302-222-22-2-22-20-200020000−2i−2i2i2i0022−2−2-2-2220000002i−2i2−200−i2−i2i2i20000−2−22200000000i2−i2000
χ312-222-22-2-22-20-200020000−2i−2i2i2i00−2−22222-2-2000000−2i2i−2200i2i2−i2−i20000−2−22200000000i2−i2000
χ322-222-22-2-22-20-200020000−2i−2i2i2i00−2−222-2-2220000002i−2i−2200i2i2−i2−i2000022−2−200000000−i2i2000
χ332-22-22-22-200-2022-202i2i−2i−2i0000002i−2i2i−2ii2−i2i2−i200002-20000i2−i2000022−2−22−22−20000000000i2−i20
χ342-22-22-22-200-2022-202i2i−2i−2i0000002i−2i2i−2i−i2i2−i2i200002-20000−i2i20000−2−222−22−220000000000−i2i20
χ352-22-22-22-200-2022-202i2i−2i−2i000000−2i2i−2i2ii2−i2i2−i20000-220000i2−i2000022−2−2−22−220000000000−i2i20
χ362-22-22-22-200-2022-202i2i−2i−2i000000−2i2i−2i2i−i2i2−i2i20000-220000−i2i20000−2−2222−22−20000000000i2−i20
χ372-22-22-22-200-2022-20−2i−2i2i2i0000002i−2i2i−2ii2−i2i2−i20000-220000i2−i20000−2−2222−22−20000000000−i2i20
χ382-22-22-22-200-2022-20−2i−2i2i2i0000002i−2i2i−2i−i2i2−i2i20000-220000−i2i2000022−2−2−22−220000000000i2−i20
χ392-22-22-22-200-2022-20−2i−2i2i2i000000−2i2i−2i2ii2−i2i2−i200002-20000i2−i20000−2−222−22−220000000000i2−i20
χ402-22-22-22-200-2022-20−2i−2i2i2i000000−2i2i−2i2i−i2i2−i2i200002-20000−i2i2000022−2−22−22−20000000000−i2i20
χ412-2-2-2-2222222-2-22-2-22-22-200002-2000000002-200000000002i−2i2i−2i0000000002i−2i0000000000
χ422-2-2-2-2222222-2-22-2-22-22-200002-2000000002-20000000000−2i2i−2i2i000000000−2i2i0000000000
χ432-2-2-2-2222222-2-22-2-2-22-2200002-200000000-2200000000002i−2i2i−2i000000000−2i2i0000000000
χ442-2-2-2-2222222-2-22-2-2-22-2200002-200000000-220000000000−2i2i−2i2i0000000002i−2i0000000000
χ452-2-2-2-2222-2-222-22-222-22-22-22-2-2200000000-222-2000000000000000000000000002-200000
χ462-2-2-2-2222-2-222-22-222-22-2-22-22-2200000000-22-2200000000000000000000000000-2200000
χ472-2-2-2-2222-2-222-22-22-22-222-22-2-22000000002-22-200000000000000000000000000-2200000
χ482-2-2-2-2222-2-222-22-22-22-22-22-22-22000000002-2-22000000000000000000000000002-200000
χ492-2-2-2-2222-2-2-222-22200002-22-22-20000000000-220000000000002-22-2000000002-20000000
χ502-2-2-2-2222-2-2-222-22200002-22-22-20000000000-22000000000000-22-2200000000-220000000
χ512-2-2-2-2222-2-2-222-2220000-22-222-200000000002-20000000000002-22-200000000-220000000
χ522-2-2-2-2222-2-2-222-2220000-22-222-200000000002-2000000000000-22-22000000002-20000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ55444-4-4-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ56444-4-4-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ57444-4-4-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ5844-44-4-44-400404-4-40000000000000000000000000000000000022−22−222200000000000000000
χ5944-44-4-44-400404-4-400000000000000000000000000000000000−222222−2200000000000000000
χ6044-44-4-44-400-40-44404i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6144-44-4-44-400-40-4440−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ6244-4-444-4-44-404000-400000000000000000000000000000022−22−2222000000000000000000000
χ6344-4-444-4-44-404000-4000000000000000000000000000000−222222−22000000000000000000000
χ6444-4-444-4-4-440-4000400004i−4i−4i4i00000000000000000000000000000000000000000000000
χ6544-4-444-4-4-440-400040000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ664-444-44-4-4-4404000-400000000002222−22−22000000000000−2222000000000000000000000000000
χ674-444-44-4-4-4404000-40000000000−22−22222200000000000022−22000000000000000000000000000
χ684-44-44-44-40040-4-440000000000000002i2−2i22i2−2i20000000000−2i22i20000000000000000000000000
χ694-44-44-44-40040-4-44000000000000000−2i22i2−2i22i200000000002i2−2i20000000000000000000000000
χ704-4-4-4-444444-4-44-44-400000000-44000000000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

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