Finite Group Databasebeta

← Group #444000

Character table — Group #444000

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444888888882244444444448888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-11-1-1-1-1-11-1-1-111-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-1-1-1-11-1-1-1-111
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1111-111-1-11-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1111-1-1-11-1-11111
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111111-11-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-111111-1-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-11-1-111-11-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-1-1111-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-11111-1-11111-1-1-1-1
χ1722222222-2-2-2-222-22-2-2-2200002222000022-2-20000000000-2-20000000200000-2000000
χ1822222222-2-2-2-222-22-2-2-22000022220000-2-2220000000000-2-20000000-2000002000000
χ1922222222-2-2-2-222-22-2-2-220000-2-2-2-2000022-2-20000000000220000000-2000002000000
χ2022222222-2-2-2-222-22-2-2-220000-2-2-2-20000-2-2220000000000220000000200000-2000000
χ2122222222-2-2-2-2-2-22-2222-22222000022-2-200000000-2-2000000000000-20000020000000
χ2222222222-2-2-2-2-2-22-2222-222220000-2-22200000000-2-2000000000000200000-20000000
χ2322222222-2-2-2-2-2-22-2222-2-2-2-2-2000022-2-20000000022000000000000200000-20000000
χ2422222222-2-2-2-2-2-22-2222-2-2-2-2-20000-2-2220000000022000000000000-20000020000000
χ2522-222-2-2-222-2-2222-22-2-2-2000000002-22-2000000000022-2-20000002-200000000000000
χ2622-222-2-2-222-2-2222-22-2-2-2000000002-22-20000000000-2-222000000-2200000000000000
χ2722-222-2-2-222-2-2222-22-2-2-200000000-22-22000000000022-2-2000000-2200000000000000
χ2822-222-2-2-222-2-2222-22-2-2-200000000-22-220000000000-2-2220000002-200000000000000
χ2922-222-2-2-222-2-2-2-2-22-22220000000000002i−2i2i−2i00000000000022-2-20000002i−2i00000000
χ3022-222-2-2-222-2-2-2-2-22-22220000000000002i−2i2i−2i000000000000-2-222000000−2i2i00000000
χ3122-222-2-2-222-2-2-2-2-22-2222000000000000−2i2i−2i2i00000000000022-2-2000000−2i2i00000000
χ3222-222-2-2-222-2-2-2-2-22-2222000000000000−2i2i−2i2i000000000000-2-2220000002i−2i00000000
χ3322-222-2-2-2-2-222-2-2222-2-22000000002-2-222i−2i−2i2i000000000000000000002i−2i0000000000
χ3422-222-2-2-2-2-222-2-2222-2-22000000002-2-22−2i2i2i−2i00000000000000000000−2i2i0000000000
χ3522-222-2-2-2-2-222-2-2222-2-2200000000-222-22i−2i−2i2i00000000000000000000−2i2i0000000000
χ3622-222-2-2-2-2-222-2-2222-2-2200000000-222-2−2i2i2i−2i000000000000000000002i−2i0000000000
χ372-222-2-22-22-22-22-2-2-222-222i2i−2i−2i22-2-2000000002i2i−2i−2i2i−2i00002-200000000000000000000
χ382-222-2-22-22-22-22-2-2-222-222i2i−2i−2i-2-22200000000−2i−2i2i2i2i−2i0000-2200000000000000000000
χ392-222-2-22-22-22-22-2-2-222-22−2i−2i2i2i22-2-200000000−2i−2i2i2i−2i2i00002-200000000000000000000
χ402-222-2-22-22-22-22-2-2-222-22−2i−2i2i2i-2-222000000002i2i−2i−2i−2i2i0000-2200000000000000000000
χ412-222-2-22-2-22-222-22-2-2-222000022-2-2000000000000002i−2i2i−2i-220000000000000000002i−2i
χ422-222-2-22-2-22-222-22-2-2-222000022-2-200000000000000−2i2i−2i2i-22000000000000000000−2i2i
χ432-222-2-22-2-22-222-22-2-2-2220000-2-222000000000000002i−2i2i−2i2-2000000000000000000−2i2i
χ442-222-2-22-2-22-222-22-2-2-2220000-2-22200000000000000−2i2i−2i2i2-20000000000000000002i−2i
χ452-222-2-22-2-22-22-22-2222-2-22i2i−2i−2i0000000000000000−2i2i0000002i−2i2i−2i0000000000002-200
χ462-222-2-22-2-22-22-22-2222-2-22i2i−2i−2i0000000000000000−2i2i000000−2i2i−2i2i000000000000-2200
χ472-222-2-22-2-22-22-22-2222-2-2−2i−2i2i2i00000000000000002i−2i0000002i−2i2i−2i000000000000-2200
χ482-222-2-22-2-22-22-22-2222-2-2−2i−2i2i2i00000000000000002i−2i000000−2i2i−2i2i0000000000002-200
χ492-2-22-22-22-222-22-222-22-2-200000000000000000000002i−2i−2i2i002i−2i−2i2i00000000002-20000
χ502-2-22-22-22-222-22-222-22-2-200000000000000000000002i−2i−2i2i00−2i2i2i−2i0000000000-220000
χ512-2-22-22-22-222-22-222-22-2-20000000000000000000000−2i2i2i−2i002i−2i−2i2i0000000000-220000
χ522-2-22-22-22-222-22-222-22-2-20000000000000000000000−2i2i2i−2i00−2i2i2i−2i00000000002-20000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5444-444-4-4-4-4-44444-4-4-444-4000000000000000000000000000000000000000000000000
χ5544-4-4-444-40000000000002i2−2i22i2−2i222−2222−22000000002i−2i2i−2i0000000000000000000000000000
χ5644-4-4-444-40000000000002i2−2i22i2−2i2−2222−222200000000−2i2i−2i2i0000000000000000000000000000
χ5744-4-4-444-4000000000000−2i22i2−2i22i222−2222−2200000000−2i2i−2i2i0000000000000000000000000000
χ5844-4-4-444-4000000000000−2i22i2−2i22i2−2222−2222000000002i−2i2i−2i0000000000000000000000000000
χ594-444-4-44-44-44-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ604-4-44-44-444-4-444-4-444-44-4000000000000000000000000000000000000000000000000
χ614-4-44-44-444-4-44-444-4-44-44000000000000000000000000000000000000000000000000
χ624-4-44-44-44-444-4-44-4-44-444000000000000000000000000000000000000000000000000
χ634-4-4-44-44400000000000022−22−222222−22−2222000000002-2-220000000000000000000000000000
χ644-4-4-44-44400000000000022−22−2222−222222−2200000000-222-20000000000000000000000000000
χ654-4-4-44-444000000000000−222222−2222−22−222200000000-222-20000000000000000000000000000
χ664-4-4-44-444000000000000−222222−22−222222−22000000002-2-220000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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