Finite Group Databasebeta

← Group #418320

Character table — Group #418320

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422224444444444448888888888882224444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-11111
χ31111111111111111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111111-1-1
χ511111111111111111111-1-11111-1-111111111111111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-111-1-1-1-1
χ711111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-111-1-111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-11111-1-1-1-111
χ9111111111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-11-1111111-1-1-1-1
χ10111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ11111111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1111-1111-1-1-1-1-1-111
χ12111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ13111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-11-11-1-111-1-11111
χ14111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-111-1-1111111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111-11-1-1-1-1-11111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11111111-1-111-1-1
χ17222222-2-2-2-222-2-2-2-222002-22-2002-22-200000000000000002000-200000000000
χ18222222-2-2-2-222-2-2-2-222002-2-22002-2-220000000000000000-2000200000000000
χ19222222-2-2-2-222-2-2-2-22200-222-200-222-20000000000000000-2000200000000000
χ20222222-2-2-2-222-2-2-2-22200-22-2200-22-2200000000000000002000-200000000000
χ212222-2-22-22-22-22-22-22-20000220000-2-20000000022-2-2000002-20000000000000
χ222222-2-22-22-22-22-22-22-20000220000-2-200000000-2-22200000-220000000000000
χ232222-2-22-22-22-22-22-22-20000-2-20000220000000022-2-200000-220000000000000
χ242222-2-22-22-22-22-22-22-20000-2-200002200000000-2-222000002-20000000000000
χ252222-2-22-22-2-22-22-22-22222-200-2-2-220000000000000000000000000000002-200
χ262222-2-22-22-2-22-22-22-2222-2200-2-22-2000000000000000000000000000000-2200
χ272222-2-22-22-2-22-22-22-22-2-22-20022-22000000000000000000000000000000-2200
χ282222-2-22-22-2-22-22-22-22-2-2-2200222-20000000000000000000000000000002-200
χ292222-2-2-22-222-2-22-222-200002-20000-2200000000000022-2-200020-20000000000
χ302222-2-2-22-222-2-22-222-200002-20000-22000000000000-2-222000-2020000000000
χ312222-2-2-22-222-2-22-222-20000-2200002-200000000000022-2-2000-2020000000000
χ322222-2-2-22-222-2-22-222-20000-2200002-2000000000000-2-22200020-20000000000
χ332222-2-2-22-22-222-22-2-2200220000-2-20022-2-2000000000000000000000000002-2
χ342222-2-2-22-22-222-22-2-2200220000-2-200-2-22200000000000000000000000000-22
χ352222-2-2-22-22-222-22-2-2200-2-20000220022-2-200000000000000000000000000-22
χ362222-2-2-22-22-222-22-2-2200-2-200002200-2-222000000000000000000000000002-2
χ372-22-22-22-2-22-2222-2-22-20000000000002i−2i2i−2i000000002-22-200000000002i−2i0000
χ382-22-22-22-2-22-2222-2-22-20000000000002i−2i2i−2i00000000-22-220000000000−2i2i0000
χ392-22-22-22-2-22-2222-2-22-2000000000000−2i2i−2i2i000000002-22-20000000000−2i2i0000
χ402-22-22-22-2-22-2222-2-22-2000000000000−2i2i−2i2i00000000-22-2200000000002i−2i0000
χ412-22-22-2-222-22-222-2-2-222-200002-2000000002i2i−2i−2i2i−2i2i−2i00000000000000000000
χ422-22-22-2-222-22-222-2-2-222-200002-200000000−2i−2i2i2i−2i2i−2i2i00000000000000000000
χ432-22-22-2-222-22-222-2-2-22-220000-22000000002i2i−2i−2i−2i2i−2i2i00000000000000000000
χ442-22-22-2-222-22-222-2-2-22-220000-2200000000−2i−2i2i2i2i−2i2i−2i00000000000000000000
χ452-22-2-22-2-222222-2-22-2-20000000000002i−2i−2i2i00002i−2i−2i2i0000000000002-2000000
χ462-22-2-22-2-222222-2-22-2-20000000000002i−2i−2i2i0000−2i2i2i−2i000000000000-22000000
χ472-22-2-22-2-222222-2-22-2-2000000000000−2i2i2i−2i00002i−2i−2i2i000000000000-22000000
χ482-22-2-22-2-222222-2-22-2-2000000000000−2i2i2i−2i0000−2i2i2i−2i0000000000002-2000000
χ492-22-2-22-2-222-2-2-222-2222-20000-2200000000000000002-2-220000002-200000000
χ502-22-2-22-2-222-2-2-222-2222-20000-220000000000000000-222-2000000-2200000000
χ512-22-2-22-2-222-2-2-222-222-2200002-200000000000000002-2-22000000-2200000000
χ522-22-2-22-2-222-2-2-222-222-2200002-20000000000000000-222-20000002-200000000
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ54444444-4-4-4-4-4-44444-4-400000000000000000000000000000000000000000000
χ554-44-44-44-4-444-4-4-444-4400000000000000000000000000000000000000000000
χ564-44-44-4-444-4-44-4-4444-400000000000000000000000000000000000000000000
χ574-44-4-4444-4-444-444-4-4-400000000000000000000000000000000000000000000
χ584-44-4-4444-4-4-4-44-4-444400000000000000000000000000000000000000000000
χ5988-8-80000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ6088-8-8000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ618-8-8800000000000000000000000000000022−22−2222000000000000000000000000
χ628-8-88000000000000000000000000000000−222222−22000000000000000000000000

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