Finite Group Databasebeta

← Group #417709

Character table — Group #417709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12222222222244444444888822222244444444444444888888888822444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111
χ5111111111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111
χ1111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-11111-1-111-1-111
χ1722222222-2-2-2-222-2-22-22-20000220022-2-2000000-2-2000022-2-200000000000000000000
χ1822222222-2-2-2-222-2-22-22-200002200-2-2-2-2000000220000-2-22200000000000000000000
χ1922222222-2-2-2-222-2-22-22-20000-2-2002222000000-2-20000-2-22200000000000000000000
χ2022222222-2-2-2-222-2-22-22-20000-2-200-2-22200000022000022-2-200000000000000000000
χ2122222222-2-2-2-2-2-222-22-22222200220000-2-200000000000000-2-20000002-20000000000
χ2222222222-2-2-2-2-2-222-22-22222200-2-200002200000000000000-2-2000000-220000000000
χ2322222222-2-2-2-2-2-222-22-22-2-2-2-200220000-2-20000000000000022000000-220000000000
χ2422222222-2-2-2-2-2-222-22-22-2-2-2-200-2-200002200000000000000220000002-20000000000
χ2522-2-2-22-2222-2-2222-2-22-2-20000002-200002-200000000000000002i2i−2i−2i0000002i−2i000000
χ2622-2-2-22-2222-2-2222-2-22-2-20000002-200002-20000000000000000−2i−2i2i2i000000−2i2i000000
χ2722-2-2-22-2222-2-2222-2-22-2-2000000-220000-2200000000000000002i2i−2i−2i000000−2i2i000000
χ2822-2-2-22-2222-2-2222-2-22-2-2000000-220000-220000000000000000−2i−2i2i2i0000002i−2i000000
χ2922-2-2-22-2222-2-2-2-2-222-222000000002-2000022-2-22-20000000000000000000000002-200
χ3022-2-2-22-2222-2-2-2-2-222-222000000002-20000-2-2222-2000000000000000000000000-2200
χ3122-2-2-22-2222-2-2-2-2-222-22200000000-22000022-2-2-22000000000000000000000000-2200
χ3222-2-2-22-2222-2-2-2-2-222-22200000000-220000-2-222-220000000000000000000000002-200
χ3322-2-2-22-22-2-222-2-22-2222-20000002-22-200-220000-220000000000000000002-200000000
χ3422-2-2-22-22-2-222-2-22-2222-20000002-2-2200-2200002-2000000000000000000-2200000000
χ3522-2-2-22-22-2-222-2-22-2222-2000000-222-2002-20000-22000000000000000000-2200000000
χ3622-2-2-22-22-2-222-2-22-2222-2000000-22-22002-200002-20000000000000000002-200000000
χ372-22-2-2-2222-2-222-22-2-2-222000000000000002-22-20000000000002-22-20000000000002-2
χ382-22-2-2-2222-2-222-22-2-2-222000000000000002-22-2000000000000-22-22000000000000-22
χ392-22-2-2-2222-2-222-22-2-2-22200000000000000-22-220000000000002-22-2000000000000-22
χ402-22-2-2-2222-2-222-22-2-2-22200000000000000-22-22000000000000-22-220000000000002-2
χ412-2-222-2-222-22-22-2222-2-2-200002-200002-2000000002i2i−2i−2i0000002i−2i−2i2i00000000000000
χ422-2-222-2-222-22-22-2222-2-2-200002-200002-200000000−2i−2i2i2i000000−2i2i2i−2i00000000000000
χ432-2-222-2-222-22-22-2222-2-2-20000-220000-22000000002i2i−2i−2i000000−2i2i2i−2i00000000000000
χ442-2-222-2-222-22-22-2222-2-2-20000-220000-2200000000−2i−2i2i2i0000002i−2i−2i2i00000000000000
χ452-2-222-2-222-22-2-22-2-2-222222-2-200000000002-2-2200000000002-200002-2000000000000
χ462-2-222-2-222-22-2-22-2-2-222222-2-20000000000-222-200000000002-20000-22000000000000
χ472-2-222-2-222-22-2-22-2-2-2222-2-22200000000002-2-220000000000-220000-22000000000000
χ482-2-222-2-222-22-2-22-2-2-2222-2-2220000000000-222-20000000000-2200002-2000000000000
χ492-2-222-2-22-22-222-2-2-222-2222-2-22-20000-220000000000000000-220000000000002-20000
χ502-2-222-2-22-22-222-2-2-222-2222-2-2-2200002-20000000000000000-22000000000000-220000
χ512-2-222-2-22-22-222-2-2-222-22-2-2222-20000-2200000000000000002-2000000000000-220000
χ522-2-222-2-22-22-222-2-2-222-22-2-222-2200002-200000000000000002-20000000000002-20000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5444-44-4-44-40000000000002i2−2i22i2−2i200000000000000002i−2i2i−2i22−220000000000000000000000
χ5544-44-4-44-40000000000002i2−2i22i2−2i20000000000000000−2i2i−2i2i−22220000000000000000000000
χ5644-44-4-44-4000000000000−2i22i2−2i22i200000000000000002i−2i2i−2i−22220000000000000000000000
χ5744-44-4-44-4000000000000−2i22i2−2i22i20000000000000000−2i2i−2i2i22−220000000000000000000000
χ5844-4-4-44-44-4-44444-44-4-4-44000000000000000000000000000000000000000000000000
χ594-444-44-4-40000000000002i2−2i2−2i22i200000000000000002-2-22002i2−2i200000000000000000000
χ604-444-44-4-40000000000002i2−2i2−2i22i20000000000000000-222-200−2i22i200000000000000000000
χ614-444-44-4-4000000000000−2i22i22i2−2i200000000000000002-2-2200−2i22i200000000000000000000
χ624-444-44-4-4000000000000−2i22i22i2−2i20000000000000000-222-2002i2−2i200000000000000000000
χ634-44-4-4-4444-4-44-44-4444-4-4000000000000000000000000000000000000000000000000
χ644-44-4-4-444-444-44-4-44-444-4000000000000000000000000000000000000000000000000
χ654-44-4-4-444-444-4-444-44-4-44000000000000000000000000000000000000000000000000
χ664-4-444-4-44-44-44-4444-4-44-4000000000000000000000000000000000000000000000000
χ67888-88-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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