Finite Group Databasebeta

← Group #278321

Character table — Group #278321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222244444444444444444888888888888888888888161616161616161632323232
order12222244444422444444444888888888888888888888888888244488882488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111-11-1
χ611111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-11
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-11-11-1
χ9111111111111-1-1111-1-1-1-1-1-11111111-1-11111-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ10111111111111-1-1111-1-1-1-1-1-11111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-111-1-111
χ11111111111111-1-1111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-111
χ12111111111111-1-1111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-11111-1-1
χ13111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ14111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-111-1
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-11
χ172222222-222-2222-2-2-2-2-2-2-22222-2-2-2-22220000-2-2000000000000000000000000
χ182222222-222-2222-2-2-2-2-2-2-222-2-22222-2-2-2000022000000000000000000000000
χ192222222-222-22-2-2-2-2-22222-2-222-2-2-2-22-2-2000022000000000000000000000000
χ202222222-222-22-2-2-2-2-22222-2-2-2-22222-2220000-2-2000000000000000000000000
χ212222-2-222-2-222222-2-222-2-2-2-20000000000000000000000000002-200002-20000
χ222222-2-222-2-222222-2-222-2-2-2-2000000000000000000000000000-220000-220000
χ232222-2-222-2-222-2-22-2-2-2-222220000000000000000000000000002-20000-220000
χ242222-2-222-2-222-2-22-2-2-2-22222000000000000000000000000000-2200002-20000
χ252222-2-22-2-2-2-2222-222-2-222-2-2000000000000000000000000000002i−2i2i−2i000000
χ262222-2-22-2-2-2-2222-222-2-222-2-200000000000000000000000000000−2i2i−2i2i000000
χ272222-2-22-2-2-2-22-2-2-22222-2-222000000000000000000000000000002i−2i−2i2i000000
χ282222-2-22-2-2-2-22-2-2-22222-2-22200000000000000000000000000000−2i2i2i−2i000000
χ292222-2-2-22222-200-22-20000002222-2-2-200222200-2-20000-2-20000000000000000
χ302222-2-2-22222-200-22-20000002222-2-2-200-2-2-2-200220000220000000000000000
χ312222-2-2-22222-200-22-2000000-2-2-2-22220022-2-200-2-20000220000000000000000
χ322222-2-2-22222-200-22-2000000-2-2-2-222200-2-22200220000-2-20000000000000000
χ332222-2-2-2-222-2-2002-2200000022-2-222-200000000002i2i−2i−2i002i2i−2i−2i000000000000
χ342222-2-2-2-222-2-2002-2200000022-2-222-20000000000−2i−2i2i2i00−2i−2i2i2i000000000000
χ352222-2-2-2-222-2-2002-22000000-2-222-2-2200000000002i2i−2i−2i00−2i−2i2i2i000000000000
χ362222-2-2-2-222-2-2002-22000000-2-222-2-220000000000−2i−2i2i2i002i2i−2i−2i000000000000
χ372-2-222-220-220-2000002i−2i2i−2i00002-22-202i−2i2−22−2002−2i2−i2i2−i22−2i2−i2i2−i2000000000000
χ382-2-222-220-220-2000002i−2i2i−2i00002-22-202i−2i−22−2200−22−i2i2−i2i2−22−i2i2−i2i2000000000000
χ392-2-222-220-220-2000002i−2i2i−2i0000-22-220−2i2i2−2−22002−2i2−i2i2−i2−22−i2i2−i2i2000000000000
χ402-2-222-220-220-2000002i−2i2i−2i0000-22-220−2i2i−222−200−22−i2i2−i2i22−2i2−i2i2−i2000000000000
χ412-2-222-220-220-200000−2i2i−2i2i00002-22-20−2i2i2−22−2002−2−i2i2−i2i22−2−i2i2−i2i2000000000000
χ422-2-222-220-220-200000−2i2i−2i2i00002-22-20−2i2i−22−2200−22i2−i2i2−i2−22i2−i2i2−i2000000000000
χ432-2-222-220-220-200000−2i2i−2i2i0000-22-2202i−2i2−2−22002−2−i2i2−i2i2−22i2−i2i2−i2000000000000
χ442-2-222-220-220-200000−2i2i−2i2i0000-22-2202i−2i−222−200−22i2−i2i2−i22−2−i2i2−i2i2000000000000
χ452-2-22-22-20-22022-200000002-2002-2-220002−22−22-2−222−2−22−22−222−2000000000000
χ462-2-22-22-20-22022-200000002-2002-2-22000−22−222-22−2−222−22−22−2−22000000000000
χ472-2-22-22-20-22022-200000002-200-222-20002−2−22-22−222−2−222−22−2−22000000000000
χ482-2-22-22-20-22022-200000002-200-222-2000−222−2-222−2−222−2−22−222−2000000000000
χ492-2-22-22-20-2202-220000000-22002-2-220002−22−2-22−22−222−2−222−2−22000000000000
χ502-2-22-22-20-2202-220000000-22002-2-22000−22−22-222−22−2−222−2−222−2000000000000
χ512-2-22-22-20-2202-220000000-2200-222-20002−2−222-2−22−222−22−2−222−2000000000000
χ522-2-22-22-20-2202-220000000-2200-222-2000−222−22-22−22−2−22−222−2−22000000000000
χ53444444-44-4-44-400-4-44000000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40044-4000000000000000000000000000000000000000000000
χ554-4-444-4-404-4044-40000000-44000000000000000000000000000000000000000
χ564-4-444-4-404-404-4400000004-4000000000000000000000000000000000000000
χ574-4-44-44404-40-4000004i−4i−4i4i00000000000000000000000000000000000000000
χ584-4-44-44404-40-400000−4i4i4i−4i00000000000000000000000000000000000000000
χ5988-8-800000000000000000004i2−4i20000000000000000000000000000000000000
χ6088-8-80000000000000000000−4i24i20000000000000000000000000000000000000
χ618-88-8000800-8000000000000000000000000000000000000000000000000000
χ628-88-8000-8008000000000000000000000000000000000000000000000000000

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