Finite Group Databasebeta

← Group #325643

Character table — Group #325643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444444448888888844444444448888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111
χ11111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ12111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-11-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-11-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1111-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-1-11-11
χ172222222222-2-2-222-2-2-2222200000000-2-222-2-222-2-20000000000000000000000000000
χ182222222222-2-2-222-2-2-2222200000000-2-2-2-222-2-2220000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-2000000002222-2-2-2-2220000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-20000000022-2-22222-2-20000000000000000000000000000
χ2122222222-2-2222-2-22-2-222-2-22222-2-2-2-22-2000000002200000000-2-20000000000000000
χ2222222222-2-2222-2-22-2-222-2-2-2-2-2-222222-200000000-2-200000000220000000000000000
χ2322222222-2-2222-2-22-2-2-2-2222222-2-2-2-2-2200000000-2-200000000220000000000000000
χ2422222222-2-2222-2-22-2-2-2-222-2-2-2-22222-22000000002200000000-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-200000000-22000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-200000000-2200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2722222222-2-2-2-2-2-2-2-222-2-222000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2822222222-2-2-2-2-2-2-2-222-2-222000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2922-2-2-2-2222-222-22-2-22-2000022-2-222-2-200000000000000002i2i−2i−2i0000000000002i−2i0000
χ3022-2-2-2-2222-222-22-2-22-2000022-2-222-2-20000000000000000−2i−2i2i2i000000000000−2i2i0000
χ3122-2-2-2-2222-222-22-2-22-20000-2-222-2-22200000000000000002i2i−2i−2i000000000000−2i2i0000
χ3222-2-2-2-2222-222-22-2-22-20000-2-222-2-2220000000000000000−2i−2i2i2i0000000000002i−2i0000
χ3322-2-2-2-222-2222-2-22-2-22000022-2-2-2-2220000000000002i2i−2i−2i000000000000002i−2i000000
χ3422-2-2-2-222-2222-2-22-2-22000022-2-2-2-222000000000000−2i−2i2i2i00000000000000−2i2i000000
χ3522-2-2-2-222-2222-2-22-2-220000-2-22222-2-20000000000002i2i−2i−2i00000000000000−2i2i000000
χ3622-2-2-2-222-2222-2-22-2-220000-2-22222-2-2000000000000−2i−2i2i2i000000000000002i−2i000000
χ372-222-2-22-22-2000-220002i−2i2i−2i2−22−22−22−200002i−2i002-2i2−i200000000i2−i2i2−i2i2−i22−22−200000000
χ382-222-2-22-22-2000-220002i−2i2i−2i2−22−22−22−20000−2i2i00-22i2−i200000000i2−i2−i2i2−i2i2−22−2200000000
χ392-222-2-22-22-2000-220002i−2i2i−2i−22−22−22−2200002i−2i002-2−i2i200000000−i2i2−i2i2−i2i2−22−2200000000
χ402-222-2-22-22-2000-220002i−2i2i−2i−22−22−22−220000−2i2i00-22−i2i200000000−i2i2i2−i2i2−i22−22−200000000
χ412-222-2-22-22-2000-22000−2i2i−2i2i2−22−22−22−200002i−2i00-22−i2i200000000−i2i2i2−i2i2−i2−22−2200000000
χ422-222-2-22-22-2000-22000−2i2i−2i2i2−22−22−22−20000−2i2i002-2−i2i200000000−i2i2−i2i2−i2i22−22−200000000
χ432-222-2-22-22-2000-22000−2i2i−2i2i−22−22−22−2200002i−2i00-22i2−i200000000i2−i2−i2i2−i2i22−22−200000000
χ442-222-2-22-22-2000-22000−2i2i−2i2i−22−22−22−220000−2i2i002-2i2−i200000000i2−i2i2−i2i2−i2−22−2200000000
χ452-222-2-22-2-220002-20002i−2i−2i2i2−22−2−22−22002-2002i−2i00i2−i200000000−i2i22−2−22−i2i2i2−i200000000
χ462-222-2-22-2-220002-20002i−2i−2i2i2−22−2−22−2200-2200−2i2i00i2−i200000000−i2i2−222−2i2−i2−i2i200000000
χ472-222-2-22-2-220002-20002i−2i−2i2i−22−222−22−2002-2002i−2i00−i2i200000000i2−i2−222−2i2−i2−i2i200000000
χ482-222-2-22-2-220002-20002i−2i−2i2i−22−222−22−200-2200−2i2i00−i2i200000000i2−i22−2−22−i2i2i2−i200000000
χ492-222-2-22-2-220002-2000−2i2i2i−2i2−22−2−22−22002-200−2i2i00−i2i200000000i2−i22−2−22i2−i2−i2i200000000
χ502-222-2-22-2-220002-2000−2i2i2i−2i2−22−2−22−2200-22002i−2i00−i2i200000000i2−i2−222−2−i2i2i2−i200000000
χ512-222-2-22-2-220002-2000−2i2i2i−2i−22−222−22−2002-200−2i2i00i2−i200000000−i2i2−222−2−i2i2i2−i200000000
χ522-222-2-22-2-220002-2000−2i2i2i−2i−22−222−22−200-22002i−2i00i2−i200000000−i2i22−2−22i2−i2−i2i200000000
χ5344-4-4-4-4444-4-4-444-44-4400000000000000000000000000000000000000000000000000
χ5444-4-4-4-444-44-4-44-4444-400000000000000000000000000000000000000000000000000
χ554-44-44-4-44004-4400-4000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ564-44-44-4-44004-4400-400000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ574-44-44-4-4400-44-400400000000000000000000000000000022−2222−22000000000000000000
χ584-44-44-4-4400-44-4004000000000000000000000000000000−2222−2222000000000000000000
χ594-4-44-44-44004-4-40040000000000000000000000000022−22−22220000000000000000000000
χ604-4-44-44-44004-4-400400000000000000000000000000−222222−220000000000000000000000
χ614-4-44-44-4400-44400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ624-4-44-44-4400-44400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000
χ634-4-4-4444-444000-4-4000000022−22−222222−22−222200000000000000000000000000000000000000
χ644-4-4-4444-444000-4-40000000−222222−22−222222−2200000000000000000000000000000000000000
χ654-4-4-4444-4-4-400044000000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4444-4-4-4000440000000−222222−2222−22−222200000000000000000000000000000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ6888-888-8-8-8000000000000000000000000000000000000000000000000000000000000

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