Finite Group Databasebeta

← Group #428392

Character table — Group #428392

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444222222444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ6111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111
χ7111111111111111111111111-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ1111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1311111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1722222222-2-2-2-222-2-22-22-20000002200000022-2-2-2-200000000000022-2-2000000000000
χ1822222222-2-2-2-222-2-22-22-200000022000000-2-222-2-2000000000000-2-222000000000000
χ1922222222-2-2-2-222-2-22-22-2000000-2-200000022-2-222000000000000-2-222000000000000
χ2022222222-2-2-2-222-2-22-22-2000000-2-2000000-2-2222200000000000022-2-2000000000000
χ2122222222-2-2-2-2-2-222-22-2200002200-2-222-2-20000000000000022-2-20000000000000000
χ2222222222-2-2-2-2-2-222-22-2200002200-2-2-2-22200000000000000-2-2220000000000000000
χ2322222222-2-2-2-2-2-222-22-220000-2-2002222-2-200000000000000-2-2220000000000000000
χ2422222222-2-2-2-2-2-222-22-220000-2-20022-2-2220000000000000022-2-20000000000000000
χ2522-222-2-2-222-2-22-2-2-222-2222-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622-222-2-2-222-2-22-2-2-222-2222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722-222-2-2-222-2-22-2-2-222-22-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2822-222-2-2-222-2-22-2-2-222-22-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292-222-2-2-222-22-2222-2-2-2-2200002-2002-200002i−2i2i−2i0000000000000000002i−2i0000000000
χ302-222-2-2-222-22-2222-2-2-2-2200002-2002-20000−2i2i−2i2i000000000000000000−2i2i0000000000
χ312-222-2-2-222-22-2222-2-2-2-220000-2200-2200002i−2i2i−2i000000000000000000−2i2i0000000000
χ322-222-2-2-222-22-2222-2-2-2-220000-2200-220000−2i2i−2i2i0000000000000000002i−2i0000000000
χ332-222-2-2-22-22-2222-22-22-2-2000000000000002i−2i−2i2i002-22-200000000000000002i−2i000000
χ342-222-2-2-22-22-2222-22-22-2-2000000000000002i−2i−2i2i00-22-220000000000000000−2i2i000000
χ352-222-2-2-22-22-2222-22-22-2-200000000000000−2i2i2i−2i002-22-20000000000000000−2i2i000000
χ362-222-2-2-22-22-2222-22-22-2-200000000000000−2i2i2i−2i00-22-2200000000000000002i−2i000000
χ372-222-2-2-22-22-22-2-22-22-2222-22-22-200-22000000000000000000000000000000002-20000
χ382-222-2-2-22-22-22-2-22-22-2222-22-2-22002-200000000000000000000000000000000-220000
χ392-222-2-2-22-22-22-2-22-22-222-22-222-200-2200000000000000000000000000000000-220000
χ402-222-2-2-22-22-22-2-22-22-222-22-22-22002-2000000000000000000000000000000002-20000
χ412-2-22-222-22-2-22-222-222-2-20000002i−2i002-22-200002i−2i0000000000000000002i−2i00000000
χ422-2-22-222-22-2-22-222-222-2-20000002i−2i00-22-2200002i−2i000000000000000000−2i2i00000000
χ432-2-22-222-22-2-22-222-222-2-2000000−2i2i002-22-20000−2i2i000000000000000000−2i2i00000000
χ442-2-22-222-22-2-22-222-222-2-2000000−2i2i00-22-220000−2i2i0000000000000000002i−2i00000000
χ452-2-22-222-2-222-22-22-2-222-200000000002-2-220000002i−2i−2i2i00000000000000000000002i−2i
χ462-2-22-222-2-222-22-22-2-222-200000000002-2-22000000−2i2i2i−2i0000000000000000000000−2i2i
χ472-2-22-222-2-222-22-22-2-222-20000000000-222-20000002i−2i−2i2i0000000000000000000000−2i2i
χ482-2-22-222-2-222-22-22-2-222-20000000000-222-2000000−2i2i2i−2i00000000000000000000002i−2i
χ492-2-22-222-2-222-2-22-222-2-222-2-22002i−2i0000000000−2i2i0000000000000000000000002i−2i00
χ502-2-22-222-2-222-2-22-222-2-222-2-2200−2i2i00000000002i−2i000000000000000000000000−2i2i00
χ512-2-22-222-2-222-2-22-222-2-22-222-2002i−2i0000000000−2i2i000000000000000000000000−2i2i00
χ522-2-22-222-2-222-2-22-222-2-22-222-200−2i2i00000000002i−2i0000000000000000000000002i−2i00
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5444-444-4-4-444-4-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ5544-444-4-4-4-4-4444-4444-4-4-4000000000000000000000000000000000000000000000000
χ5644-444-4-4-4-4-444-44-4-4-4444000000000000000000000000000000000000000000000000
χ574-444-4-4-444-44-4-4-4-44444-4000000000000000000000000000000000000000000000000
χ584-44-444-4-40000000000000000000000000000000000002i−2i2i−2i22−2200002i2−2i2000000000000
χ594-44-444-4-40000000000000000000000000000000000002i−2i2i−2i−22220000−2i22i2000000000000
χ604-44-444-4-4000000000000000000000000000000000000−2i2i−2i2i22−220000−2i22i2000000000000
χ614-44-444-4-4000000000000000000000000000000000000−2i2i−2i2i−222200002i2−2i2000000000000
χ624-4-44-444-44-4-444-4-44-4-444000000000000000000000000000000000000000000000000
χ634-4-4-44-4440000000000000000000000000000000000002-2-220022−2222−2200000000000000
χ644-4-4-44-4440000000000000000000000000000000000002-2-2200−2222−222200000000000000
χ654-4-4-44-444000000000000000000000000000000000000-222-20022−22−222200000000000000
χ664-4-4-44-444000000000000000000000000000000000000-222-200−222222−2200000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ6888-8-8-88-88000000000000000000000000000000000000000000000000000000000000

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