Finite Group Databasebeta

← Group #429573

Character table — Group #429573

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222888888888888888888888888161616161616161616161616161616161616
order12224444222222444444224444448888888888888888244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1-1-1
χ911111111111111111111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ172222-2-2-2-22-2-22-2-222-222-2000000002i2i−2i−2i00002i2i−2i−2i00002-20000000000000000
χ182222-2-2-2-22-2-22-2-222-222-2000000002i2i−2i−2i0000−2i−2i2i2i0000-220000000000000000
χ192222-2-2-2-22-2-22-2-222-222-200000000−2i−2i2i2i00002i2i−2i−2i0000-220000000000000000
χ202222-2-2-2-22-2-22-2-222-222-200000000−2i−2i2i2i0000−2i−2i2i2i00002-20000000000000000
χ212222-2-2-2-2-22-2-22-22-222-22000022-2-200002i2i−2i−2i00000000000000002i−2i00000000
χ222222-2-2-2-2-22-2-22-22-222-22000022-2-20000−2i−2i2i2i0000000000000000−2i2i00000000
χ232222-2-2-2-2-22-2-22-22-222-220000-2-22200002i2i−2i−2i0000000000000000−2i2i00000000
χ242222-2-2-2-2-22-2-22-22-222-220000-2-2220000−2i−2i2i2i00000000000000002i−2i00000000
χ252222-2-2-2-2-2-22-2-22-222-22222-2-200000000000000002i2i−2i−2i0000002i−2i0000000000
χ262222-2-2-2-2-2-22-2-22-222-22222-2-20000000000000000−2i−2i2i2i000000−2i2i0000000000
χ272222-2-2-2-2-2-22-2-22-222-222-2-22200000000000000002i2i−2i−2i000000−2i2i0000000000
χ282222-2-2-2-2-2-22-2-22-222-222-2-2220000000000000000−2i−2i2i2i0000002i−2i0000000000
χ292-2-2222-2-22-2-2-222-2-2-22222-22-22-22-2000000000000000000000000002-2000000
χ302-2-2222-2-22-2-2-222-2-2-22222-22-2-22-2200000000000000000000000000-22000000
χ312-2-2222-2-22-2-2-222-2-2-2222-22-222-22-200000000000000000000000000-22000000
χ322-2-2222-2-22-2-2-222-2-2-2222-22-22-22-22000000000000000000000000002-2000000
χ332-2-2222-2-2-22-22-22-2222-2-2000000002i−2i2i−2i000000002-22-2000000000000002i−2i00
χ342-2-2222-2-2-22-22-22-2222-2-2000000002i−2i2i−2i00000000-22-2200000000000000−2i2i00
χ352-2-2222-2-2-22-22-22-2222-2-200000000−2i2i−2i2i000000002-22-200000000000000−2i2i00
χ362-2-2222-2-2-22-22-22-2222-2-200000000−2i2i−2i2i00000000-22-22000000000000002i−2i00
χ372-2-2222-2-2-2-2222-22-22-22-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000002-20000
χ382-2-2222-2-2-2-2222-22-22-22-20000000000002i−2i2i−2i−2i2i−2i2i0000000000000000-220000
χ392-2-2222-2-2-2-2222-22-22-22-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000-220000
χ402-2-2222-2-2-2-2222-22-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000002-20000
χ412-2-22-2-2222-2-2-222222-2-2-20000000000002-2-2200002i−2i−2i2i00000000000000002i−2i
χ422-2-22-2-2222-2-2-222222-2-2-20000000000002-2-220000−2i2i2i−2i0000000000000000−2i2i
χ432-2-22-2-2222-2-2-222222-2-2-2000000000000-222-200002i−2i−2i2i0000000000000000−2i2i
χ442-2-22-2-2222-2-2-222222-2-2-2000000000000-222-20000−2i2i2i−2i00000000000000002i−2i
χ452-2-22-2-222-22-22-222-2-2-2222-2-220000000000002-2-22000000002-2000000000000
χ462-2-22-2-222-22-22-222-2-2-2222-2-22000000000000-222-200000000-22000000000000
χ472-2-22-2-222-22-22-222-2-2-222-222-20000000000002-2-2200000000-22000000000000
χ482-2-22-2-222-22-22-222-2-2-222-222-2000000000000-222-2000000002-2000000000000
χ492-2-22-2-222-2-2222-2-22-22-2200002-2-222-2-22000000000000002-200000000000000
χ502-2-22-2-222-2-2222-2-22-22-2200002-2-22-222-200000000000000-2200000000000000
χ512-2-22-2-222-2-2222-2-22-22-220000-222-22-2-2200000000000000-2200000000000000
χ522-2-22-2-222-2-2222-2-22-22-220000-222-2-222-2000000000000002-200000000000000
χ53444444444-4-44-4-4-4-44-4-44000000000000000000000000000000000000000000
χ5444444444-44-4-44-4-44-4-44-4000000000000000000000000000000000000000000
χ5544444444-4-44-4-444-4-44-4-4000000000000000000000000000000000000000000
χ564444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000
χ574-4-4444-4-4444-4-4-444-4-4-44000000000000000000000000000000000000000000
χ584-4-44-4-444444-4-4-4-4-4444-4000000000000000000000000000000000000000000
χ5988-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000
χ6088-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000
χ618-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000
χ628-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000

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