Finite Group Databasebeta

← Group #418874

Character table — Group #418874

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222222888888888888888888888888888816161616161616161616161616161616
order12222222224444444422222222224444448888888888884444444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ311111111111111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ51111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ9111111111111111111-1-1-1-111-1-11111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ10111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ13111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ14111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1
χ1722222-2-22-2-2222-22-2-2-20000220000-2-20000000000002i2i−2i−2i000000002i−2i000000
χ1822222-2-22-2-2222-22-2-2-20000220000-2-2000000000000−2i−2i2i2i00000000−2i2i000000
χ1922222-2-22-2-2222-22-2-2-20000-2-20000220000000000002i2i−2i−2i00000000−2i2i000000
χ2022222-2-22-2-2222-22-2-2-20000-2-2000022000000000000−2i−2i2i2i000000002i−2i000000
χ2122222-2-22-2-2-2-2-22-2222000000220000-2-20022-2-2000000002-200000000000000
χ2222222-2-22-2-2-2-2-22-2222000000220000-2-200-2-22200000000-2200000000000000
χ2322222-2-22-2-2-2-2-22-2222000000-2-20000220022-2-200000000-2200000000000000
χ2422222-2-22-2-2-2-2-22-2222000000-2-200002200-2-222000000002-200000000000000
χ252222-22-2-2-222-2-2-2222-222-2-20000220000-2-20000000000000000002-200000000
χ262222-22-2-2-222-2-2-2222-222-2-20000-2-2000022000000000000000000-2200000000
χ272222-22-2-2-222-2-2-2222-2-2-2220000220000-2-2000000000000000000-2200000000
χ282222-22-2-2-222-2-2-2222-2-2-2220000-2-20000220000000000000000002-200000000
χ292-2-2222-2-22-2-22-2222-2-200002-200002-200002i−2i2i−2i2i2i−2i−2i00000000000000000000
χ302-2-2222-2-22-2-22-2222-2-200002-200002-20000−2i2i−2i2i−2i−2i2i2i00000000000000000000
χ312-2-2222-2-22-2-22-2222-2-20000-220000-2200002i−2i2i−2i−2i−2i2i2i00000000000000000000
χ322-2-2222-2-22-2-22-2222-2-20000-220000-220000−2i2i−2i2i2i2i−2i−2i00000000000000000000
χ332-2-222-22-2-222-222-22-2-22-22-20000000000002i−2i−2i2i00000000002i−2i000000000000
χ342-2-222-22-2-222-222-22-2-22-22-2000000000000−2i2i2i−2i0000000000−2i2i000000000000
χ352-2-222-22-2-222-222-22-2-2-22-220000000000002i−2i−2i2i0000000000−2i2i000000000000
χ362-2-222-22-2-222-222-22-2-2-22-22000000000000−2i2i2i−2i00000000002i−2i000000000000
χ372-2-222-22-2-22-22-2-22-22200002-2002-2-22002-200000000000000000000002-20000
χ382-2-222-22-2-22-22-2-22-22200002-200-22-2200-220000000000000000000000-220000
χ392-2-222-22-2-22-22-2-22-2220000-22002-22-2002-20000000000000000000000-220000
χ402-2-222-22-2-22-22-2-22-2220000-2200-222-200-2200000000000000000000002-20000
χ412-2-22-2222-2-222-22-2-22-20000002-200002-200000000002i−2i2i−2i0000000000002i−2i00
χ422-2-22-2222-2-222-22-2-22-20000002-200002-20000000000−2i2i−2i2i000000000000−2i2i00
χ432-2-22-2222-2-222-22-2-22-2000000-220000-2200000000002i−2i2i−2i000000000000−2i2i00
χ442-2-22-2222-2-222-22-2-22-2000000-220000-220000000000−2i2i−2i2i0000000000002i−2i00
χ452-2-22-2-2-222222-2-2-22-222-2-22000000000000000000002-2-2200002-20000000000
χ462-2-22-2-2-222222-2-2-22-222-2-2200000000000000000000-222-20000-220000000000
χ472-2-22-2-2-222222-2-2-22-22-222-2000000000000000000002-2-220000-220000000000
χ482-2-22-2-2-222222-2-2-22-22-222-200000000000000000000-222-200002-20000000000
χ492-2-22-2-2-2222-2-2222-22-20000002-22-200-22-22000000000000000000000000002-2
χ502-2-22-2-2-2222-2-2222-22-20000002-2-2200-222-200000000000000000000000000-22
χ512-2-22-2-2-2222-2-2222-22-2000000-222-2002-2-2200000000000000000000000000-22
χ522-2-22-2-2-2222-2-2222-22-2000000-22-22002-22-2000000000000000000000000002-2
χ534444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ544444-44-4-4-44-4444-4-4-4400000000000000000000000000000000000000000000
χ554444-4-44-44-44-4-444-4-4400000000000000000000000000000000000000000000
χ564444-4-44-44-4-444-4-444-400000000000000000000000000000000000000000000
χ574-4-4444-4-44-44-44-4-4-44400000000000000000000000000000000000000000000
χ584-4-44-4444-4-4-4-44-444-4400000000000000000000000000000000000000000000
χ5988-8-800000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ6088-8-80000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ618-88-8000000000000000000000000000000000022−22−222200000000000000000000
χ628-88-80000000000000000000000000000000000−222222−2200000000000000000000

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