Finite Group Databasebeta

← Group #319621

Character table — Group #319621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444444444444224488888888888888888888888844888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ911111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ1011111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-111-1-111-1-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-111-1-1111-1-11
χ172222222222-2-2-2-2-2-2-2-22222-2-200000000000000002222-2-2-2-2-220000000022-2-2000000000000
χ182222222222-2-2-2-2-2-2-2-22222-2-20000000000000000-2-2-2-22222-2200000000-2-222000000000000
χ192222222222-2-2-2-2-2-2-2-222-2-22200000000000000002222-2-2-2-22-200000000-2-222000000000000
χ202222222222-2-2-2-2-2-2-2-222-2-2220000000000000000-2-2-2-222222-20000000022-2-2000000000000
χ2122222222-2-22222-2-2-2-2-2-22222000000002222-2-2-2-200000000-2-2000022-2-20000000000000000
χ2222222222-2-22222-2-2-2-2-2-2222200000000-2-2-2-2222200000000-2-20000-2-2220000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000220000-2-2220000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-2-2-222220000000022000022-2-20000000000000000
χ2522222222-2-2-2-2-2-22222-2-222-2-22222-2-2-2-200000000000000002-222-2-200000000000000000000
χ2622222222-2-2-2-2-2-22222-2-222-2-2-2-2-2-2222200000000000000002-2-2-22200000000000000000000
χ2722222222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-20000000000000000-22-2-22200000000000000000000
χ2822222222-2-2-2-2-2-22222-2-2-2-222-2-2-2-222220000000000000000-2222-2-200000000000000000000
χ292222-2-2-2-20022-2-20000002-22-222−2−222−2−2000022-2-222−2−222−2−2002−22−2002-22−22−2000000000000
χ302222-2-2-2-20022-2-20000002-22-222−2−222−2−20000-2-222−2−222−2−222002−22−200-22−22−22000000000000
χ312222-2-2-2-20022-2-20000002-22-2−2−222−2−222000022-2-2−2−222−2−22200−22−22002-2−22−22000000000000
χ322222-2-2-2-20022-2-20000002-22-2−2−222−2−2220000-2-22222−2−222−2−200−22−2200-222−22−2000000000000
χ332222-2-2-2-20022-2-2000000-22-2222−2−222−2−2000022-2-222−2−222−2−200−22−2200-22−22−22000000000000
χ342222-2-2-2-20022-2-2000000-22-2222−2−222−2−20000-2-222−2−222−2−22200−22−22002-22−22−2000000000000
χ352222-2-2-2-20022-2-2000000-22-22−2−222−2−222000022-2-2−2−222−2−222002−22−200-222−22−2000000000000
χ362222-2-2-2-20022-2-2000000-22-22−2−222−2−2220000-2-22222−2−222−2−2002−22−2002-2−22−22000000000000
χ372222-2-2-2-200-2-2220000002-2-2222−2−2−2−22222-2-2000022−2−2−2−222002−2−222-2002−2−22000000000000
χ382222-2-2-2-200-2-2220000002-2-2222−2−2−2−222-2-2220000−2−22222−2−2002−2−22-2200−222−2000000000000
χ392222-2-2-2-200-2-2220000002-2-22−2−22222−2−222-2-20000−2−22222−2−200−222−22-200−222−2000000000000
χ402222-2-2-2-200-2-2220000002-2-22−2−22222−2−2-2-222000022−2−2−2−22200−222−2-22002−2−22000000000000
χ412222-2-2-2-200-2-222000000-222-222−2−2−2−22222-2-2000022−2−2−2−22200−222−2-2200−222−2000000000000
χ422222-2-2-2-200-2-222000000-222-222−2−2−2−222-2-2220000−2−22222−2−200−222−22-2002−2−22000000000000
χ432222-2-2-2-200-2-222000000-222-2−2−22222−2−222-2-20000−2−22222−2−2002−2−22-22002−2−22000000000000
χ442222-2-2-2-200-2-222000000-222-2−2−22222−2−2-2-222000022−2−2−2−222002−2−222-200−222−2000000000000
χ452-2-222-2-22222-22-222-2-2-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000002i−2i002-2000000
χ462-2-222-2-22222-22-222-2-2-2-2000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000−2i2i00-22000000
χ472-2-222-2-22222-22-222-2-2-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000002i−2i00-22000000
χ482-2-222-2-22222-22-222-2-2-2-200000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000−2i2i002-2000000
χ492-2-222-2-2222-22-22-2-222-2-2000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000002i−2i002-20000
χ502-2-222-2-2222-22-22-2-222-2-2000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000−2i2i00-220000
χ512-2-222-2-2222-22-22-2-222-2-200000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000002i−2i00-220000
χ522-2-222-2-2222-22-22-2-222-2-200000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000−2i2i002-20000
χ5344-4-444-4-40000004-44-40000000000000022−2222−2222−2222−220000000000000000000000000000000000
χ5444-4-444-4-40000004-44-400000000000000−2222−2222−2222−22220000000000000000000000000000000000
χ5544-4-444-4-4000000-44-440000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ5644-4-444-4-4000000-44-4400000000000000−2222−222222−2222−220000000000000000000000000000000000
χ5744-4-4-4-4444-4000000004-400000000000022−22−222222−22−22220000000000000000000000000000000000
χ5844-4-4-4-4444-4000000004-4000000000000−222222−22−222222−220000000000000000000000000000000000
χ5944-4-4-4-444-4400000000-4400000000000022−22−2222−222222−220000000000000000000000000000000000
χ6044-4-4-4-444-4400000000-44000000000000−222222−2222−22−22220000000000000000000000000000000000
χ614-44-44-44-40000004-4-440000004-44-40000000000000000000000000000000000000000000000
χ624-44-44-44-40000004-4-44000000-44-440000000000000000000000000000000000000000000000
χ634-44-44-44-4000000-444-400000000004-44-4000000000000000000000000000000000000000000
χ644-44-44-44-4000000-444-40000000000-44-44000000000000000000000000000000000000000000
χ654-44-4-44-444-400000000-44000022−22−222222−22−2222000000000000000000000000000000000000000000
χ664-44-4-44-444-400000000-440000−222222−22−222222−22000000000000000000000000000000000000000000
χ674-44-4-44-44-44000000004-4000022−22−2222−222222−22000000000000000000000000000000000000000000
χ684-44-4-44-44-44000000004-40000−222222−2222−22−2222000000000000000000000000000000000000000000
χ694-4-444-4-44-4-44-44-4-4-44444000000000000000000000000000000000000000000000000000000
χ704-4-444-4-44-4-4-44-4444-4-444000000000000000000000000000000000000000000000000000000
χ714-4-44-444-4004-4-44000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ724-4-44-444-4004-4-4400000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ734-4-44-444-400-444-4000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ744-4-44-444-400-444-400000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000

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