Finite Group Databasebeta

← Group #450830

Character table — Group #450830

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444222244444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ5111111111111111111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-111-1-111-1-1
χ1722222222-2-2-2-22-2222-2-2-200000000000022-2-2000022-2-20000000022-2-2000000000000
χ1822222222-2-2-2-22-2222-2-2-200000000000022-2-20000-2-22200000000-2-222000000000000
χ1922222222-2-2-2-22-2222-2-2-2000000000000-2-222000022-2-200000000-2-222000000000000
χ2022222222-2-2-2-22-2222-2-2-2000000000000-2-2220000-2-2220000000022-2-2000000000000
χ2122222222-2-2-2-2-22-2-2-22220000220000-2-2000022-2-20000000022-2-20000000000000000
χ2222222222-2-2-2-2-22-2-2-22220000220000-2-20000-2-22200000000-2-2220000000000000000
χ2322222222-2-2-2-2-22-2-2-22220000-2-2000022000022-2-200000000-2-2220000000000000000
χ2422222222-2-2-2-2-22-2-2-22220000-2-20000220000-2-2220000000022-2-20000000000000000
χ2522-222-2-2-222-2-2-2-222-222-200002i−2i00002i−2i000000002i−2i2i−2i0000000000002-20000000000
χ2622-222-2-2-222-2-2-2-222-222-200002i−2i00002i−2i00000000−2i2i−2i2i000000000000-220000000000
χ2722-222-2-2-222-2-2-2-222-222-20000−2i2i0000−2i2i000000002i−2i2i−2i000000000000-220000000000
χ2822-222-2-2-222-2-2-2-222-222-20000−2i2i0000−2i2i00000000−2i2i−2i2i0000000000002-20000000000
χ2922-222-2-2-2-2-2222-2-2-2222-222-2-22i−2i0000−2i2i00000000000000000000000000002i−2i000000
χ3022-222-2-2-2-2-2222-2-2-2222-222-2-2−2i2i00002i−2i0000000000000000000000000000−2i2i000000
χ3122-222-2-2-2-2-2222-2-2-2222-2-2-2222i−2i0000−2i2i0000000000000000000000000000−2i2i000000
χ3222-222-2-2-2-2-2222-2-2-2222-2-2-222−2i2i00002i−2i00000000000000000000000000002i−2i000000
χ3322-222-2-2-2-2-222-2222-2-2-2200000022-2-200000000002i−2i−2i2i00000000000000000000002i−2i
χ3422-222-2-2-2-2-222-2222-2-2-2200000022-2-20000000000−2i2i2i−2i0000000000000000000000−2i2i
χ3522-222-2-2-2-2-222-2222-2-2-22000000-2-22200000000002i−2i−2i2i0000000000000000000000−2i2i
χ3622-222-2-2-2-2-222-2222-2-2-22000000-2-2220000000000−2i2i2i−2i00000000000000000000002i−2i
χ372-22-222-2-22-22-22-22-2-22-222-22-2000000002i−2i2i−2i000000000000000000000000002i−2i0000
χ382-22-222-2-22-22-22-22-2-22-222-22-200000000−2i2i−2i2i00000000000000000000000000−2i2i0000
χ392-22-222-2-22-22-22-22-2-22-22-22-22000000002i−2i2i−2i00000000000000000000000000−2i2i0000
χ402-22-222-2-22-22-22-22-2-22-22-22-2200000000−2i2i−2i2i000000000000000000000000002i−2i0000
χ412-22-222-2-22-22-2-22-222-22-20000002i−2i2i−2i0000002i−2i2i−2i0000000000000000000000002-200
χ422-22-222-2-22-22-2-22-222-22-20000002i−2i2i−2i000000−2i2i−2i2i000000000000000000000000-2200
χ432-22-222-2-22-22-2-22-222-22-2000000−2i2i−2i2i0000002i−2i2i−2i000000000000000000000000-2200
χ442-22-222-2-22-22-2-22-222-22-2000000−2i2i−2i2i000000−2i2i−2i2i0000000000000000000000002-200
χ452-22-222-2-2-22-22222-2-2-22-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000002-200000000
χ462-22-222-2-2-22-22222-2-2-22-20000000000002i−2i−2i2i−2i2i2i−2i000000000000000000-2200000000
χ472-22-222-2-2-22-22222-2-2-22-2000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000-2200000000
χ482-22-222-2-2-22-22222-2-2-22-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000002-200000000
χ492-2-2-22-222-222-222-22-22-2-22-2-22002i−2i−2i2i000000000000002i2i−2i−2i00000000000000000000
χ502-2-2-22-222-222-222-22-22-2-22-2-2200−2i2i2i−2i00000000000000−2i−2i2i2i00000000000000000000
χ512-2-2-22-222-222-222-22-22-2-2-222-2002i−2i−2i2i00000000000000−2i−2i2i2i00000000000000000000
χ522-2-2-22-222-222-222-22-22-2-2-222-200−2i2i2i−2i000000000000002i2i−2i−2i00000000000000000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ5444-444-4-4-444-4-444-4-44-4-44000000000000000000000000000000000000000000000000
χ5544-4-4-444-40000000000000000000000000000000000002i−2i2i−2i2i2−2i20022−2200000000000000
χ5644-4-4-444-40000000000000000000000000000000000002i−2i2i−2i−2i22i200−222200000000000000
χ5744-4-4-444-4000000000000000000000000000000000000−2i2i−2i2i2i2−2i200−222200000000000000
χ5844-4-4-444-4000000000000000000000000000000000000−2i2i−2i2i−2i22i20022−2200000000000000
χ594-444-4-44-40000000000000000000000000000000000002-2-22002i2−2i2002i2−2i2000000000000
χ604-444-4-44-40000000000000000000000000000000000002-2-2200−2i22i200−2i22i2000000000000
χ614-444-4-44-4000000000000000000000000000000000000-222-2002i2−2i200−2i22i2000000000000
χ624-444-4-44-4000000000000000000000000000000000000-222-200−2i22i2002i2−2i2000000000000
χ634-44-444-4-4-44-44-4-4-4444-44000000000000000000000000000000000000000000000000
χ644-4-4-44-4444-4-444-4-44-4-444000000000000000000000000000000000000000000000000
χ654-4-4-44-4444-4-44-444-444-4-4000000000000000000000000000000000000000000000000
χ664-4-4-44-444-444-4-4-44-44-444000000000000000000000000000000000000000000000000
χ67888-8-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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