Finite Group Databasebeta

← Group #429643

Character table — Group #429643

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12222222222244444444888822444444444444444444888888888824444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-111111111
χ5111111111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ1111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-111111-1-1-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111
χ1722222222-2-2-2-22-2222-2-2-20000220022-2-2000000-2-2000000000022-2-200000000000000
χ1822222222-2-2-2-22-2222-2-2-200002200-2-2-2-2000000220000000000-2-22200000000000000
χ1922222222-2-2-2-22-2222-2-2-20000-2-2002222000000-2-20000000000-2-22200000000000000
χ2022222222-2-2-2-22-2222-2-2-20000-2-200-2-22200000022000000000022-2-200000000000000
χ2122222222-2-2-2-2-22-2-2-2222222200220000-2-20000000000-2-200000000200-20000000000
χ2222222222-2-2-2-2-22-2-2-2222222200-2-20000220000000000-2-200000000-20020000000000
χ2322222222-2-2-2-2-22-2-2-2222-2-2-2-200220000-2-200000000002200000000-20020000000000
χ2422222222-2-2-2-2-22-2-2-2222-2-2-2-200-2-200002200000000002200000000200-20000000000
χ2522-22-22-2-222-2-2-2-222-222-20000002i−2i2i−2i002i−2i00002i−2i0000000000000002-200000000000
χ2622-22-22-2-222-2-2-2-222-222-20000002i−2i−2i2i002i−2i0000−2i2i000000000000000-2200000000000
χ2722-22-22-2-222-2-2-2-222-222-2000000−2i2i2i−2i00−2i2i00002i−2i000000000000000-2200000000000
χ2822-22-22-2-222-2-2-2-222-222-2000000−2i2i−2i2i00−2i2i0000−2i2i0000000000000002-200000000000
χ2922-22-22-2-2-2-2222-2-2-2222-20000002i−2i0000−2i2i00000000000022-2-200000000002i−2i000000
χ3022-22-22-2-2-2-2222-2-2-2222-20000002i−2i0000−2i2i000000000000-2-2220000000000−2i2i000000
χ3122-22-22-2-2-2-2222-2-2-2222-2000000−2i2i00002i−2i00000000000022-2-20000000000−2i2i000000
χ3222-22-22-2-2-2-2222-2-2-2222-2000000−2i2i00002i−2i000000000000-2-22200000000002i−2i000000
χ3322-22-22-2-2-2-222-2222-2-2-22000000002i−2i00002i2i−2i−2i−2i2i0000000000000000000000002-200
χ3422-22-22-2-2-2-222-2222-2-2-22000000002i−2i0000−2i−2i2i2i−2i2i000000000000000000000000-2200
χ3522-22-22-2-2-2-222-2222-2-2-2200000000−2i2i00002i2i−2i−2i2i−2i000000000000000000000000-2200
χ3622-22-22-2-2-2-222-2222-2-2-2200000000−2i2i0000−2i−2i2i2i2i−2i0000000000000000000000002-200
χ372-22-2-222-22-22-22-22-2-22-2200002-200002-2000000002i2i−2i−2i002i−2i2i−2i000000000000000000
χ382-22-2-222-22-22-22-22-2-22-2200002-200002-200000000−2i−2i2i2i00−2i2i−2i2i000000000000000000
χ392-22-2-222-22-22-22-22-2-22-220000-220000-22000000002i2i−2i−2i00−2i2i−2i2i000000000000000000
χ402-22-2-222-22-22-22-22-2-22-220000-220000-2200000000−2i−2i2i2i002i−2i2i−2i000000000000000000
χ412-22-2-222-22-22-2-22-222-22-22i2i−2i−2i00000000002i−2i2i−2i0000002i−2i0000000000002-200000000
χ422-22-2-222-22-22-2-22-222-22-22i2i−2i−2i0000000000−2i2i−2i2i0000002i−2i000000000000-2200000000
χ432-22-2-222-22-22-2-22-222-22-2−2i−2i2i2i00000000002i−2i2i−2i000000−2i2i000000000000-2200000000
χ442-22-2-222-22-22-2-22-222-22-2−2i−2i2i2i0000000000−2i2i−2i2i000000−2i2i0000000000002-200000000
χ452-22-2-222-2-22-22222-2-2-22-22i2i−2i−2i2-20000-22000000000000−2i2i00000000000000002i−2i0000
χ462-22-2-222-2-22-22222-2-2-22-22i2i−2i−2i-2200002-2000000000000−2i2i0000000000000000−2i2i0000
χ472-22-2-222-2-22-22222-2-2-22-2−2i−2i2i2i2-20000-220000000000002i−2i0000000000000000−2i2i0000
χ482-22-2-222-2-22-22222-2-2-22-2−2i−2i2i2i-2200002-20000000000002i−2i00000000000000002i−2i0000
χ492-2-2-222-22-222-222-22-22-2-2000000000000002-2-22000000002i−2i−2i2i00000000000000002i−2i
χ502-2-2-222-22-222-222-22-22-2-2000000000000002-2-2200000000−2i2i2i−2i0000000000000000−2i2i
χ512-2-2-222-22-222-222-22-22-2-200000000000000-222-2000000002i−2i−2i2i0000000000000000−2i2i
χ522-2-2-222-22-222-222-22-22-2-200000000000000-222-200000000−2i2i2i−2i00000000000000002i−2i
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-44-4-4-400000000000022−2222−2200000000000000002-22-200000022−220000000000000000
χ55444-44-4-4-400000000000022−2222−220000000000000000-22-22000000−22220000000000000000
χ56444-44-4-4-4000000000000−2222−222200000000000000002-22-2000000−22220000000000000000
χ57444-44-4-4-4000000000000−2222−22220000000000000000-22-2200000022−220000000000000000
χ5844-44-44-4-444-4-444-4-44-4-44000000000000000000000000000000000000000000000000
χ594-444-4-4-440000000000002i2−2i2−2i22i200000000000000002i−2i−2i2i0000000022−2200000000000000
χ604-444-4-4-440000000000002i2−2i2−2i22i20000000000000000−2i2i2i−2i00000000−222200000000000000
χ614-444-4-4-44000000000000−2i22i22i2−2i200000000000000002i−2i−2i2i00000000−222200000000000000
χ624-444-4-4-44000000000000−2i22i22i2−2i20000000000000000−2i2i2i−2i0000000022−2200000000000000
χ634-44-4-444-4-44-44-4-4-4444-44000000000000000000000000000000000000000000000000
χ644-4-4-444-444-4-444-4-44-4-444000000000000000000000000000000000000000000000000
χ654-4-4-444-444-4-44-444-444-4-4000000000000000000000000000000000000000000000000
χ664-4-4-444-44-444-4-4-44-44-444000000000000000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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