Finite Group Databasebeta

← Group #237803

Character table — Group #237803

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222222222444444444422222222444444448888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ911111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1111111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ1211111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1311111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1411111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1511111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ1611111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-200000000-2-222-2-2220000000000000000000000000000
χ1922222222222-2-2-2-2-2-2-2-222222-2-222-2-20000000022-2-2-2-2220000000000000000000000000000
χ2022222222222-2-2-2-2-2-2-2-222222-2-222-2-200000000-2-22222-2-20000000000000000000000000000
χ2122222222-2-2-22222-2-2-2-2-222222-2-2-22-2000000000000000000000000000000002-22-200000000
χ2222222222-2-2-22222-2-2-2-2-222222-2-2-22-200000000000000000000000000000000-22-2200000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-2-2222-220000000000000000000000000000000000002-22-20000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2-2222-22000000000000000000000000000000000000-22-220000
χ2522222222-2-2-2-2-2-2-22222-22222-22-2-2-220000000000000000000000000000000000002-2-220000
χ2622222222-2-2-2-2-2-2-22222-22222-22-2-2-22000000000000000000000000000000000000-222-20000
χ2722222222-2-2-2-2-2-2-22222-2-2-2-2-22-2222-2000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-22222-2-2-2-2-22-2222-200000000000000000000000000000000-222-200000000
χ292222-2-2-2-222-222-2-222-2-2-222-2-2222-2-2-222-2-222-2-2000000000000000000000000000000000000
χ302222-2-2-2-222-222-2-222-2-2-222-2-2222-2-2-2-2-222-2-222000000000000000000000000000000000000
χ312222-2-2-2-222-222-2-222-2-2-2-2-222-2-2-222200000000000000000000000000000000000000002i−2i2i−2i
χ322222-2-2-2-222-222-2-222-2-2-2-2-222-2-2-22220000000000000000000000000000000000000000−2i2i−2i2i
χ332222-2-2-2-222-2-2-222-2-222-222-2-2-2-22-22200000000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-222-2-2-222-2-222-222-2-2-2-22-2220000000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-222-2-2-222-2-222-2-2-22222-22-2-222-2-2-2-222000000000000000000000000000000000000
χ362222-2-2-2-222-2-2-222-2-222-2-2-22222-22-2-2-2-22222-2-2000000000000000000000000000000000000
χ372222-2-2-2-2-2-2222-2-2-2-222222-2-22-2-22-2200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ382222-2-2-2-2-2-2222-2-2-2-222222-2-22-2-22-220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ392222-2-2-2-2-2-2222-2-2-2-2222-2-222-222-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ402222-2-2-2-2-2-2222-2-2-2-2222-2-222-222-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ412222-2-2-2-2-2-22-2-22222-2-2222-2-2-22-222-20000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ422222-2-2-2-2-2-22-2-22222-2-2222-2-2-22-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ432222-2-2-2-2-2-22-2-22222-2-22-2-2222-22-2-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ442222-2-2-2-2-2-22-2-22222-2-22-2-2222-22-2-220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4522-2-222-2-22-222-22-22-22-2-2000000000000000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ4622-2-222-2-22-222-22-22-22-2-2000000000000000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ4722-2-222-2-22-222-22-22-22-2-200000000000000000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ4822-2-222-2-22-222-22-22-22-2-200000000000000000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ4922-2-222-2-22-22-22-22-22-22-2000000000000000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ5022-2-222-2-22-22-22-22-22-22-2000000000000000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ5122-2-222-2-22-22-22-22-22-22-200000000000000000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ5222-2-222-2-22-22-22-22-22-22-200000000000000000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ5322-2-2-2-222-2222-2-22-222-2-20000000000000000002i−2i002i−2i002−2−222−2−22i2−i2−i2i2i2−i2−i2i2000000000000
χ5422-2-2-2-222-2222-2-22-222-2-20000000000000000002i−2i002i−2i00−222−2−222−2−i2i2i2−i2−i2i2i2−i2000000000000
χ5522-2-2-2-222-2222-2-22-222-2-2000000000000000000−2i2i00−2i2i002−2−222−2−22−i2i2i2−i2−i2i2i2−i2000000000000
χ5622-2-2-2-222-2222-2-22-222-2-2000000000000000000−2i2i00−2i2i00−222−2−222−2i2−i2−i2i2i2−i2−i2i2000000000000
χ5722-2-2-2-222-222-222-22-2-22-20000000000000000002i−2i00−2i2i002−2−22−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ5822-2-2-2-222-222-222-22-2-22-20000000000000000002i−2i00−2i2i00−222−22−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ5922-2-2-2-222-222-222-22-2-22-2000000000000000000−2i2i002i−2i002−2−22−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ6022-2-2-2-222-222-222-22-2-22-2000000000000000000−2i2i002i−2i00−222−22−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ6144-4-444-4-4-44-44-44-4-44-444000000000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-44-4-44-444-44-44000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-44-4-444-4-444000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-4-444-4-444-44000000000000000000000000000000000000000000000000000000
χ654-4-444-44-40000000000004-44-40000002-22-22-22-2000000000000000000000000000000000000
χ664-4-444-44-40000000000004-44-4000000-22-22-22-22000000000000000000000000000000000000
χ674-4-444-44-4000000000000-44-440000002-22-2-22-22000000000000000000000000000000000000
χ684-4-444-44-4000000000000-44-44000000-22-222-22-2000000000000000000000000000000000000
χ694-4-44-44-440000000000004-4-440000002-2-222-2-22000000000000000000000000000000000000
χ704-4-44-44-440000000000004-4-44000000-222-2-222-2000000000000000000000000000000000000
χ714-4-44-44-44000000000000-444-40000002-2-22-222-2000000000000000000000000000000000000
χ724-4-44-44-44000000000000-444-4000000-222-22-2-22000000000000000000000000000000000000
χ738-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000

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