Finite Group Databasebeta

← Group #267889

Character table — Group #267889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222444444444444444488888888888888888888881616161616161616161616163232
order12222244442222444444444444244444888888888888888824448888888824
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-11
χ61111111111111111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-1111-1
χ71111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-111111-1
χ81111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-111111-1-1-1-1-11
χ91111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1
χ101111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111
χ111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ121111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111-11-11111-1-1-1-11-1
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-1-1-11111-11
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-11-111-1-1-1-111-11
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-11-11-1-11111-1-11-1
χ1722222222222222-2-222-2-2-2-222-2-2-2-2-2-222000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000
χ192222222222-2-2-2-2-2-222222222-2-2-2-222-2-2000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000
χ21222222-2-2-2-2000022220000-2-2-2-2-2200002i2i−2i−2i00002i2i−2i−2i000000000000000000
χ22222222-2-2-2-2000022220000-2-2-2-2-220000−2i−2i2i2i0000−2i−2i2i2i000000000000000000
χ23222222-2-2-2-2000022-2-2000022-2-22-200002i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ24222222-2-2-2-2000022-2-2000022-2-22-20000−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ25222222-2-2-2-20000-2-2220000-2-2222-20000000022-2-2000022-2-200000000000000
χ26222222-2-2-2-20000-2-2220000-2-2222-200000000-2-2220000-2-22200000000000000
χ27222222-2-2-2-20000-2-2-2-200002222-220000000022-2-20000-2-22200000000000000
χ28222222-2-2-2-20000-2-2-2-200002222-2200000000-2-222000022-2-200000000000000
χ292222-2-2-22-2222-2-22-20022-2-2002-20000000000000000000000020-22-200000000
χ302222-2-2-22-2222-2-22-20022-2-2002-200000000000000000000000-202-2200000000
χ312222-2-2-22-2222-2-2-2200-2-22200-22000000000000000000000020-2000002-20000
χ322222-2-2-22-2222-2-2-2200-2-22200-220000000000000000000000-20200000-220000
χ332222-2-2-22-22-2-2222-200-2-222002-20000000000000000000000020-2-2200000000
χ342222-2-2-22-22-2-2222-200-2-222002-200000000000000000000000-2022-200000000
χ352222-2-2-22-22-2-222-220022-2-200-22000000000000000000000020-200000-220000
χ362222-2-2-22-22-2-222-220022-2-200-220000000000000000000000-202000002-20000
χ372-22-22-22-2-222-22-2002i−2i00002i−2i0000002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000
χ382-22-22-22-2-222-22-2002i−2i00002i−2i0000002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000
χ392-22-22-22-2-222-22-200−2i2i0000−2i2i000000−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000
χ402-22-22-22-2-222-22-200−2i2i0000−2i2i000000−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000
χ412-22-22-22-2-22-22-22002i−2i00002i−2i000000−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−2200000000000000
χ422-22-22-22-2-22-22-22002i−2i00002i−2i000000−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−200000000000000
χ432-22-22-22-2-22-22-2200−2i2i0000−2i2i0000002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−200000000000000
χ442-22-22-22-2-22-22-2200−2i2i0000−2i2i0000002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−2200000000000000
χ452-22-22-2-222-20000002i−2i2i−2i2i−2i−2i2i00002-2002−2−22i2−i2−i2i2−i2i2i2−i22−2−2200000000000000
χ462-22-22-2-222-20000002i−2i2i−2i2i−2i−2i2i00002-200−222−2−i2i2i2−i2i2−i2−i2i2−222−200000000000000
χ472-22-22-2-222-20000002i−2i−2i2i−2i2i−2i2i0000-22002−2−22−i2i2i2−i2−i2i2i2−i2−222−200000000000000
χ482-22-22-2-222-20000002i−2i−2i2i−2i2i−2i2i0000-2200−222−2i2−i2−i2i2i2−i2−i2i22−2−2200000000000000
χ492-22-22-2-222-2000000−2i2i2i−2i2i−2i2i−2i0000-22002−2−22i2−i2−i2i2i2−i2−i2i2−222−200000000000000
χ502-22-22-2-222-2000000−2i2i2i−2i2i−2i2i−2i0000-2200−222−2−i2i2i2−i2−i2i2i2−i22−2−2200000000000000
χ512-22-22-2-222-2000000−2i2i−2i2i−2i2i2i−2i00002-2002−2−22−i2i2i2−i2i2−i2−i2i22−2−2200000000000000
χ522-22-22-2-222-2000000−2i2i−2i2i−2i2i2i−2i00002-200−222−2i2−i2−i2i2−i2i2i2−i2−222−200000000000000
χ534444-4-44-44-400004-400000000-44000000000000000000000000000000000000
χ544444-4-44-44-40000-44000000004-4000000000000000000000000000000000000
χ554-44-4-4444-4-4000000004i−4i−4i4i0000000000000000000000000000000000000000
χ564-44-4-4444-4-400000000−4i4i4i−4i0000000000000000000000000000000000000000
χ574-44-4-44-4-4444-4-44000000000000000000000000000000000000000000000000
χ584-44-4-44-4-444-444-4000000000000000000000000000000000000000000000000
χ5988-8-8000000000000000000000000000000000000000000000000002i2−2i2000000
χ6088-8-800000000000000000000000000000000000000000000000000−2i22i2000000
χ618-8-8800000000000000000000000000000000000000000000000000000022−2200
χ628-8-88000000000000000000000000000000000000000000000000000000−222200

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