Finite Group Databasebeta

← Group #449874

Character table — Group #449874

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444222244444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ3111111111111111111111111-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ51111111111111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ911111111111111111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ1011111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1111111111111111111111-1-111-1-111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1211111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111
χ1311111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1
χ1722222222-2-2-2-222-22-2-2-2222220000-2-2-2-2000000000000000022-2-20000000000000000
χ1822222222-2-2-2-222-22-2-2-2222-2-20000-2-2220000000000000000-2-2220000000000000000
χ1922222222-2-2-2-222-22-2-2-22-2-222000022-2-20000000000000000-2-2220000000000000000
χ2022222222-2-2-2-222-22-2-2-22-2-2-2-200002222000000000000000022-2-20000000000000000
χ2122222222-2-2-2-2-2-22-2222-2000022220000-2-20000-2-200000000000022-2-2000000000000
χ2222222222-2-2-2-2-2-22-2222-2000022-2-20000-2-2000022000000000000-2-222000000000000
χ2322222222-2-2-2-2-2-22-2222-20000-2-2220000220000-2-2000000000000-2-222000000000000
χ2422222222-2-2-2-2-2-22-2222-20000-2-2-2-200002200002200000000000022-2-2000000000000
χ2522-2-22-2-222-2-2222-2-222-2-2000000000000002i2i−2i−2i002i2i−2i−2i22-2-200000000000000000000
χ2622-2-22-2-222-2-2222-2-222-2-2000000000000002i2i−2i−2i00−2i−2i2i2i-2-22200000000000000000000
χ2722-2-22-2-222-2-2222-2-222-2-200000000000000−2i−2i2i2i002i2i−2i−2i-2-22200000000000000000000
χ2822-2-22-2-222-2-2222-2-222-2-200000000000000−2i−2i2i2i00−2i−2i2i2i22-2-200000000000000000000
χ292-22-222-2-222-2-22-22-22-2-220000002i−2i0000002-22-22i−2i000000000000000000002i−2i000000
χ302-22-222-2-222-2-22-22-22-2-220000002i−2i000000-22-222i−2i00000000000000000000−2i2i000000
χ312-22-222-2-222-2-22-22-22-2-22000000−2i2i0000002-22-2−2i2i00000000000000000000−2i2i000000
χ322-22-222-2-222-2-22-22-22-2-22000000−2i2i000000-22-22−2i2i000000000000000000002i−2i000000
χ332-22-222-2-222-2-2-22-22-222-22-20000002-200000000002i−2i2i−2i00000000000000000000002i−2i
χ342-22-222-2-222-2-2-22-22-222-22-20000002-20000000000−2i2i−2i2i0000000000000000000000−2i2i
χ352-22-222-2-222-2-2-22-22-222-2-22000000-2200000000002i−2i2i−2i0000000000000000000000−2i2i
χ362-22-222-2-222-2-2-22-22-222-2-22000000-220000000000−2i2i−2i2i00000000000000000000002i−2i
χ372-22-222-2-2-2-222-22222-2-2-22-200002i−2i-2200000000−2i2i0000000000000000002i−2i00000000
χ382-22-222-2-2-2-222-22222-2-2-22-20000−2i2i-22000000002i−2i000000000000000000−2i2i00000000
χ392-22-222-2-2-2-222-22222-2-2-2-2200002i−2i2-200000000−2i2i000000000000000000−2i2i00000000
χ402-22-222-2-2-2-222-22222-2-2-2-220000−2i2i2-2000000002i−2i0000000000000000002i−2i00000000
χ412-2-222-22-22-22-22-2-222-22-2002-20000002-2002i−2i−2i2i000000000000000000000000002i−2i00
χ422-2-222-22-22-22-22-2-222-22-2002-20000002-200−2i2i2i−2i00000000000000000000000000−2i2i00
χ432-2-222-22-22-22-22-2-222-22-200-22000000-22002i−2i−2i2i00000000000000000000000000−2i2i00
χ442-2-222-22-22-22-22-2-222-22-200-22000000-2200−2i2i2i−2i000000000000000000000000002i−2i00
χ452-2-222-22-22-22-2-222-2-22-2200002i−2i0000002i−2i0000002-2-220000000000000000002i−2i0000
χ462-2-222-22-22-22-2-222-2-22-2200002i−2i0000002i−2i000000-222-2000000000000000000−2i2i0000
χ472-2-222-22-22-22-2-222-2-22-220000−2i2i000000−2i2i0000002-2-22000000000000000000−2i2i0000
χ482-2-222-22-22-22-2-222-2-22-220000−2i2i000000−2i2i000000-222-20000000000000000002i−2i0000
χ492-2-222-22-2-22-222-222-22-2-2002-22i−2i0000-22−2i2i00000000000000000000002i−2i0000000000
χ502-2-222-22-2-22-222-222-22-2-2002-2−2i2i0000-222i−2i0000000000000000000000−2i2i0000000000
χ512-2-222-22-2-22-222-222-22-2-200-222i−2i00002-2−2i2i0000000000000000000000−2i2i0000000000
χ522-2-222-22-2-22-222-222-22-2-200-22−2i2i00002-22i−2i00000000000000000000002i−2i0000000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5444-4-44-4-444-4-44-4-444-4-444000000000000000000000000000000000000000000000000
χ5544-4-44-4-44-444-4444-4-4-44-4000000000000000000000000000000000000000000000000
χ5644-4-44-4-44-444-4-4-4-4444-44000000000000000000000000000000000000000000000000
χ574-444-4-4-440000000000000000000000000000000000002-22-2002i2−2i2002i2−2i2000000000000
χ584-444-4-4-440000000000000000000000000000000000002-22-200−2i22i200−2i22i2000000000000
χ594-444-4-4-44000000000000000000000000000000000000-22-22002i2−2i200−2i22i2000000000000
χ604-444-4-4-44000000000000000000000000000000000000-22-2200−2i22i2002i2−2i2000000000000
χ614-44-444-4-4-4-4444-4-4-4-4444000000000000000000000000000000000000000000000000
χ624-4-444-44-4-44-44-44-4-44-444000000000000000000000000000000000000000000000000
χ634-4-4-4-44440000000000000000000000000000000000002-2-2222−220022−2200000000000000
χ644-4-4-4-44440000000000000000000000000000000000002-2-22−222200−222200000000000000
χ654-4-4-4-4444000000000000000000000000000000000000-222-222−2200−222200000000000000
χ664-4-4-4-4444000000000000000000000000000000000000-222-2−22220022−2200000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ6888-88-88-8-8000000000000000000000000000000000000000000000000000000000000

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