Finite Group Databasebeta

← Group #419385

Character table — Group #419385

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422224444444444444444888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1
χ31111111111111111111111-1-11111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ511111111111111111111-1-11111-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1111111-1-1
χ9111111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ10111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111
χ11111111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ12111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ13111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111
χ14111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111
χ17222222-2-2-2-2222-22-2-2-2220000-2-200000000000000002i2i−2i−2i00002i−2i0000000000
χ18222222-2-2-2-2222-22-2-2-2220000-2-20000000000000000−2i−2i2i2i0000−2i2i0000000000
χ19222222-2-2-2-2222-22-2-2-2-2-200002200000000000000002i2i−2i−2i0000−2i2i0000000000
χ20222222-2-2-2-2222-22-2-2-2-2-20000220000000000000000−2i−2i2i2i00002i−2i0000000000
χ21222222-2-2-2-2-2-2-22-2222002-222002-2-2-20000000000000000000000002-2000000
χ22222222-2-2-2-2-2-2-22-2222002-2-2-2002-222000000000000000000000000-22000000
χ23222222-2-2-2-2-2-2-22-222200-222200-22-2-2000000000000000000000000-22000000
χ24222222-2-2-2-2-2-2-22-222200-22-2-200-22220000000000000000000000002-2000000
χ252222-2-222-2-22-2-2-2222-22-22-2002-2-22000000000000000000002-2000000000000
χ262222-2-222-2-22-2-2-2222-22-2-22002-22-200000000000000000000-22000000000000
χ272222-2-222-2-22-2-2-2222-2-222-200-22-2200000000000000000000-22000000000000
χ282222-2-222-2-22-2-2-2222-2-22-2200-222-2000000000000000000002-2000000000000
χ292222-2-2-2-2222-2-222-2-222-20000-220000000022-2-222-2-200000000000000000000
χ302222-2-2-2-2222-2-222-2-222-20000-2200000000-2-222-2-22200000000000000000000
χ312222-2-2-2-2222-2-222-2-22-2200002-20000000022-2-2-2-22200000000000000000000
χ322222-2-2-2-2222-2-222-2-22-2200002-200000000-2-22222-2-200000000000000000000
χ332222-2-2-2-222-222-2-222-200220000-2-20022-2-20000000000000000000000002-200
χ342222-2-2-2-222-222-2-222-200220000-2-200-2-222000000000000000000000000-2200
χ352222-2-2-2-222-222-2-222-200-2-20000220022-2-2000000000000000000000000-2200
χ362222-2-2-2-222-222-2-222-200-2-200002200-2-2220000000000000000000000002-200
χ372-22-22-22-22-222-2-2-22-220000000000002i−2i2i−2i000000002-22-20000002i−2i00000000
χ382-22-22-22-22-222-2-2-22-220000000000002i−2i2i−2i00000000-22-22000000−2i2i00000000
χ392-22-22-22-22-222-2-2-22-22000000000000−2i2i−2i2i000000002-22-2000000−2i2i00000000
χ402-22-22-22-22-222-2-2-22-22000000000000−2i2i−2i2i00000000-22-220000002i−2i00000000
χ412-22-22-22-22-2-2-2222-22-200002i−2i00002i−2i000000002i−2i2i−2i00002-200000000000000
χ422-22-22-22-22-2-2-2222-22-200002i−2i00002i−2i00000000−2i2i−2i2i0000-2200000000000000
χ432-22-22-22-22-2-2-2222-22-20000−2i2i0000−2i2i000000002i−2i2i−2i0000-2200000000000000
χ442-22-22-22-22-2-2-2222-22-20000−2i2i0000−2i2i00000000−2i2i−2i2i00002-200000000000000
χ452-22-22-2-22-2222-22-2-22-200002i−2i0000−2i2i0000000000002i−2i−2i2i000000000000002-2
χ462-22-22-2-22-2222-22-2-22-200002i−2i0000−2i2i000000000000−2i2i2i−2i00000000000000-22
χ472-22-22-2-22-2222-22-2-22-20000−2i2i00002i−2i0000000000002i−2i−2i2i00000000000000-22
χ482-22-22-2-22-2222-22-2-22-20000−2i2i00002i−2i000000000000−2i2i2i−2i000000000000002-2
χ492-22-2-22-222-2-22-2222-2-20000000000002i−2i−2i2i00002i−2i−2i2i000000000000002-20000
χ502-22-2-22-222-2-22-2222-2-20000000000002i−2i−2i2i0000−2i2i2i−2i00000000000000-220000
χ512-22-2-22-222-2-22-2222-2-2000000000000−2i2i2i−2i00002i−2i−2i2i00000000000000-220000
χ522-22-2-22-222-2-22-2222-2-2000000000000−2i2i2i−2i0000−2i2i2i−2i000000000000002-20000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-4-444-4-4-4444-4-4-4400000000000000000000000000000000000000000000
χ554-44-44-4-44-44-4-44-444-4400000000000000000000000000000000000000000000
χ564-44-4-444-4-444-444-44-4-400000000000000000000000000000000000000000000
χ574-44-4-444-4-44-44-4-44-44400000000000000000000000000000000000000000000
χ584-44-4-44-444-44-44-4-4-44400000000000000000000000000000000000000000000
χ5988-8-8000000000000000000000000000000004i−4i000000000000000000000000
χ6088-8-800000000000000000000000000000000−4i4i000000000000000000000000
χ618-8-880000000000000000000000000000004-400000000000000000000000000
χ628-8-88000000000000000000000000000000-4400000000000000000000000000

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