Finite Group Databasebeta

← Group #419376

Character table — Group #419376

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12222222222244444444888822224444444444444444888888888844444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-11111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ1111111111111111111111-1-1-1-111-1-11111-1-11111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-111-1-111
χ1722222222-2-2-2-222-2-22-22-2000000222200-2-2-2-20000000000000022-2-200000000000000
χ1822222222-2-2-2-222-2-22-22-200000022-2-200-2-22200000000000000-2-22200000000000000
χ1922222222-2-2-2-222-2-22-22-2000000-2-2220022-2-200000000000000-2-22200000000000000
χ2022222222-2-2-2-222-2-22-22-2000000-2-2-2-20022220000000000000022-2-200000000000000
χ2122222222-2-2-2-2-2-222-22-222222220000-2-2000000000000-2-2000000002-2000000000000
χ2222222222-2-2-2-2-2-222-22-222222-2-2000022000000000000-2-200000000-22000000000000
χ2322222222-2-2-2-2-2-222-22-22-2-2-2-2220000-2-20000000000002200000000-22000000000000
χ2422222222-2-2-2-2-2-222-22-22-2-2-2-2-2-200002200000000000022000000002-2000000000000
χ2522-2-2-222-222-2-22-22-22-2-22000000002i−2i00002i−2i00002i2i−2i−2i0022-2-2000000000000000000
χ2622-2-2-222-222-2-22-22-22-2-22000000002i−2i00002i−2i0000−2i−2i2i2i00-2-222000000000000000000
χ2722-2-2-222-222-2-22-22-22-2-2200000000−2i2i0000−2i2i00002i2i−2i−2i00-2-222000000000000000000
χ2822-2-2-222-222-2-22-22-22-2-2200000000−2i2i0000−2i2i0000−2i−2i2i2i0022-2-2000000000000000000
χ2922-2-2-222-222-2-2-22-22-222-22i2i−2i−2i0000000000002i2i−2i−2i00002i−2i000000000000002-2000000
χ3022-2-2-222-222-2-2-22-22-222-22i2i−2i−2i000000000000−2i−2i2i2i00002i−2i00000000000000-22000000
χ3122-2-2-222-222-2-2-22-22-222-2−2i−2i2i2i0000000000002i2i−2i−2i0000−2i2i00000000000000-22000000
χ3222-2-2-222-222-2-2-22-22-222-2−2i−2i2i2i000000000000−2i−2i2i2i0000−2i2i000000000000002-2000000
χ3322-2-2-222-2-2-2222-2-2222-2-22i2i−2i−2i00002i−2i0000−2i2i00000000−2i2i00000000000000002-20000
χ3422-2-2-222-2-2-2222-2-2222-2-22i2i−2i−2i0000−2i2i00002i−2i00000000−2i2i0000000000000000-220000
χ3522-2-2-222-2-2-2222-2-2222-2-2−2i−2i2i2i00002i−2i0000−2i2i000000002i−2i0000000000000000-220000
χ3622-2-2-222-2-2-2222-2-2222-2-2−2i−2i2i2i0000−2i2i00002i−2i000000002i−2i00000000000000002-20000
χ372-222-2-22-22-2-222-222-2-22-200000000000000002i−2i2i−2i0000002i−2i2i−2i00000000000000002-2
χ382-222-2-22-22-2-222-222-2-22-200000000000000002i−2i2i−2i000000−2i2i−2i2i0000000000000000-22
χ392-222-2-22-22-2-222-222-2-22-20000000000000000−2i2i−2i2i0000002i−2i2i−2i0000000000000000-22
χ402-222-2-22-22-2-222-222-2-22-20000000000000000−2i2i−2i2i000000−2i2i−2i2i00000000000000002-2
χ412-2-2-22-2222-22-2222-2-22-2-200002-200002-2000000000000002i−2i−2i2i0000002i−2i0000000000
χ422-2-2-22-2222-22-2222-2-22-2-200002-200002-200000000000000−2i2i2i−2i000000−2i2i0000000000
χ432-2-2-22-2222-22-2222-2-22-2-20000-220000-22000000000000002i−2i−2i2i000000−2i2i0000000000
χ442-2-2-22-2222-22-2222-2-22-2-20000-220000-2200000000000000−2i2i2i−2i0000002i−2i0000000000
χ452-2-2-22-2222-22-2-2-2-222-2220000002-200002-2002-2-220000000000000000000000002-200
χ462-2-2-22-2222-22-2-2-2-222-2220000002-200002-200-222-2000000000000000000000000-2200
χ472-2-2-22-2222-22-2-2-2-222-222000000-220000-22002-2-22000000000000000000000000-2200
χ482-2-2-22-2222-22-2-2-2-222-222000000-220000-2200-222-20000000000000000000000002-200
χ492-2-2-22-222-22-22-2-22-2222-200002-22-200-22-220000000000000000000000002-200000000
χ502-2-2-22-222-22-22-2-22-2222-200002-2-2200-222-2000000000000000000000000-2200000000
χ512-2-2-22-222-22-22-2-22-2222-20000-222-2002-2-22000000000000000000000000-2200000000
χ522-2-2-22-222-22-22-2-22-2222-20000-22-22002-22-20000000000000000000000002-200000000
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
χ5844-44-4-4-440000000000002i2−2i2−2i22i200000000000000002i−2i−2i2i0000000022−2200000000000000
χ5944-44-4-4-440000000000002i2−2i2−2i22i20000000000000000−2i2i2i−2i00000000−222200000000000000
χ6044-44-4-4-44000000000000−2i22i22i2−2i200000000000000002i−2i−2i2i00000000−222200000000000000
χ6144-44-4-4-44000000000000−2i22i22i2−2i20000000000000000−2i2i2i−2i0000000022−2200000000000000
χ6244-4-4-444-4-4-444-444-4-4-444000000000000000000000000000000000000000000000000
χ634-444-4-44-44-4-44-44-4-444-44000000000000000000000000000000000000000000000000
χ644-444-4-44-4-444-44-4-4-4-4444000000000000000000000000000000000000000000000000
χ654-444-4-44-4-444-4-44444-4-4-4000000000000000000000000000000000000000000000000
χ664-4-4-44-444-44-4444-44-4-4-44000000000000000000000000000000000000000000000000
χ678-88-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8888-8-8000000000000000000000000000000000000000000000000000000000000

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