Finite Group Databasebeta

← Group #278337

Character table — Group #278337

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444422444444444888888888888888888888888888444488884488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11-11-1
χ611111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-11-11
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11-11
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111-1-111-1-1111-11-1
χ9111111111111-1-111-1-1-1-11-1-1111111-1-111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1
χ10111111111111-1-111-1-1-1-11-1-1111111-1-111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ11111111111111-1-111-1-1-1-11-1-1111111-1-1-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-111-1-111
χ12111111111111-1-111-1-1-1-11-1-1111111-1-1-1-1-1-11-1-1-1-11111-1-11111-1-11111-1-111-1-1
χ13111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ14111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ15111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-111-1-1111111-1-1-1-11111-1-1-1-1-111-1
χ16111111111111-1-111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-111-1-1111111-1-1-1-1-1-1-1-111111-1-11
χ1722222222-222-222-2-2-2-222-2-2-22222-2-2220000-2-2-2000000000000000000000000
χ1822222222-222-222-2-2-2-222-2-2-2-2-2-2-222-2-20000222000000000000000000000000
χ1922222222-222-2-2-2-2-222-2-2-2222222-2-2-2-20000-222000000000000000000000000
χ2022222222-222-2-2-2-2-222-2-2-222-2-2-2-2222200002-2-2000000000000000000000000
χ212222-2-22-222-22002-20000-20022-2-222002222-200-2-20000-2-20000000000000000
χ222222-2-22-222-22002-20000-20022-2-22200-2-2-2-2-200220000220000000000000000
χ232222-2-22-222-22002-20000-200-2-222-2-20022-2-2200-2-20000220000000000000000
χ242222-2-22-222-22002-20000-200-2-222-2-200-2-222200220000-2-20000000000000000
χ252222-2-22-2-22-2-200-22000020022-2-2-2-2000000200002i2i−2i−2i002i2i−2i−2i000000000000
χ262222-2-22-2-22-2-200-22000020022-2-2-2-200000020000−2i−2i2i2i00−2i−2i2i2i000000000000
χ272222-2-22-2-22-2-200-220000200-2-22222000000-200002i2i−2i−2i00−2i−2i2i2i000000000000
χ282222-2-22-2-22-2-200-220000200-2-22222000000-20000−2i−2i2i2i002i2i−2i−2i000000000000
χ292222-2-2-222-22222-22-2-2-2-2-2220000000000000000000000000002-2002-2000000
χ302222-2-2-222-22222-22-2-2-2-2-222000000000000000000000000000-2200-22000000
χ312222-2-2-222-222-2-2-222222-2-2-20000000000000000000000000002-200-22000000
χ322222-2-2-222-222-2-2-222222-2-2-2000000000000000000000000000-22002-2000000
χ332222-2-2-22-2-22-2222-222-2-22-2-2000000000000000000000000000002i−2i002i−2i0000
χ342222-2-2-22-2-22-2222-222-2-22-2-200000000000000000000000000000−2i2i00−2i2i0000
χ352222-2-2-22-2-22-2-2-22-2-2-222222000000000000000000000000000002i−2i00−2i2i0000
χ362222-2-2-22-2-22-2-2-22-2-2-22222200000000000000000000000000000−2i2i002i−2i0000
χ372-22-22-2-2-2022000002i−2i0002i−2i2i−2i2i−2i0000i2−i22−202-2i2−i22−22−22−2i2−i2i2−i2000000000000
χ382-22-22-2-2-2022000002i−2i0002i−2i2i−2i2i−2i0000−i2i2−2202-2−i2i2−22−22−22−i2i2−i2i2000000000000
χ392-22-22-2-2-2022000002i−2i0002i−2i−2i2i−2i2i0000i2−i2−220-22i2−i22−22−2−22−i2i2−i2i2000000000000
χ402-22-22-2-2-2022000002i−2i0002i−2i−2i2i−2i2i0000−i2i22−20-22−i2i2−22−222−2i2−i2i2−i2000000000000
χ412-22-22-2-2-202200000−2i2i000−2i2i2i−2i2i−2i0000i2−i22−20-22i2−i2−22−222−2−i2i2−i2i2000000000000
χ422-22-22-2-2-202200000−2i2i000−2i2i2i−2i2i−2i0000−i2i2−220-22−i2i22−22−2−22i2−i2i2−i2000000000000
χ432-22-22-2-2-202200000−2i2i000−2i2i−2i2i−2i2i0000i2−i2−2202-2i2−i2−22−22−22i2−i2i2−i2000000000000
χ442-22-22-2-2-202200000−2i2i000−2i2i−2i2i−2i2i0000−i2i22−202-2−i2i22−22−22−2−i2i2−i2i2000000000000
χ452-22-2-22-2202-202-200002-20002i−2i−2i2i002i−2ii2−i22−2000−i2i2i2−i2−i2i2−22−222−2000000000000
χ462-22-2-22-2202-202-200002-20002i−2i−2i2i002i−2i−i2i2−22000i2−i2−i2i2i2−i22−22−2−22000000000000
χ472-22-2-22-2202-202-200002-2000−2i2i2i−2i00−2i2ii2−i2−22000−i2i2i2−i2−i2i22−22−2−22000000000000
χ482-22-2-22-2202-202-200002-2000−2i2i2i−2i00−2i2i−i2i22−2000i2−i2−i2i2i2−i2−22−222−2000000000000
χ492-22-2-22-2202-20-220000-220002i−2i−2i2i00−2i2ii2−i22−2000−i2i2−i2i2i2−i2−222−2−22000000000000
χ502-22-2-22-2202-20-220000-220002i−2i−2i2i00−2i2i−i2i2−22000i2−i2i2−i2−i2i22−2−222−2000000000000
χ512-22-2-22-2202-20-220000-22000−2i2i2i−2i002i−2ii2−i2−22000−i2i2−i2i2i2−i22−2−222−2000000000000
χ522-22-2-22-2202-20-220000-22000−2i2i2i−2i002i−2i−i2i22−2000i2−i2i2−i2−i2i2−222−2−22000000000000
χ53444444-4-44-4-4400-4-40000400000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-400440000-400000000000000000000000000000000000000000
χ554-44-44-4440-4-404-40000-44000000000000000000000000000000000000000000
χ564-44-44-4440-4-40-4400004-4000000000000000000000000000000000000000000
χ574-44-4-444-40-44000004i−4i000−4i4i000000000000000000000000000000000000000
χ584-44-4-444-40-4400000−4i4i0004i−4i000000000000000000000000000000000000000
χ5988-8-80000000000000000000000042−42000000000000000000000000000000000
χ6088-8-800000000000000000000000−4242000000000000000000000000000000000
χ618-8-880000800-800000000000000000000000000000000000000000000000000
χ628-8-880000-800800000000000000000000000000000000000000000000000000

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