Finite Group Databasebeta

← Group #241385

Character table — Group #241385

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444888888888888888888888888444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111
χ911111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1111-111-1-1-1-1
χ1011111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-11-1-11111
χ1111111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-1-1111-1-111
χ1211111111-1-1-1-111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1111-1-1-111-1-1
χ1311111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-11-1-111-1-1
χ1411111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-11-111-1-111
χ1511111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-1-11-1-1-11111
χ1611111111-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111-1111-1-1-1-1
χ17222222222222222-2-22222-2-22-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ18222222222222222-2-22222-2-22-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-222-2-2-2-222-2-222-2-2-2000000000000000000000000000000002-200-22000000
χ20222222222222-2-2-222-2-2-2-222-2-222-2-2-200000000000000000000000000000000-22002-2000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-222200000000000000000000000000000000002-20000002-2
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22-2-22220000000000000000000000000000000000-22000000-22
χ2322222222-2-2-2-2222-2-2-2-2-2-2-2-22-22222-222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-2-2-2-2-22-22222-2-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-222222222-2-2-2-222-2000000000000000000000000000000002200-2-2000000
χ2622222222-2-2-2-2-2-2-222222222-2-2-2-222-200000000000000000000000000000000-2-20022000000
χ2722222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-2200000000000000000000000000000000002-2000000-22
χ2822222222-2-2-2-2-2-2-2-2-22222-2-2-2222-2-220000000000000000000000000000000000-220000002-2
χ292222-2-2-2-222-2-222-22222-2-2-2-2-2-22-22-2200000000000000000000000022-2-222-2-2000000000000
χ302222-2-2-2-222-2-222-22222-2-2-2-2-2-22-22-22000000000000000000000000-2-222-2-222000000000000
χ312222-2-2-2-222-2-222-2-2-222-2-222-22-22-22-20000000022-2-222-2-20000000000000000000000000000
χ322222-2-2-2-222-2-222-2-2-222-2-222-22-22-22-200000000-2-222-2-2220000000000000000000000000000
χ332222-2-2-2-222-2-2-2-2222-2-222-2-2222-2-22-2000000000000000022-2-222-2-200000000000000000000
χ342222-2-2-2-222-2-2-2-2222-2-222-2-2222-2-22-20000000000000000-2-222-2-22200000000000000000000
χ352222-2-2-2-222-2-2-2-22-2-2-2-222222-2-222-22000000000000000000000000000000000000002i−2i2i−2i00
χ362222-2-2-2-222-2-2-2-22-2-2-2-222222-2-222-2200000000000000000000000000000000000000−2i2i−2i2i00
χ372222-2-2-2-2-2-22222-222-2-222-2-2-2-2-22-22200000000000000000000000022-2-2-2-222000000000000
χ382222-2-2-2-2-2-22222-222-2-222-2-2-2-2-22-222000000000000000000000000-2-22222-2-2000000000000
χ392222-2-2-2-2-2-22222-2-2-2-2-22222-222-22-2-20000000022-2-2-2-2220000000000000000000000000000
χ402222-2-2-2-2-2-22222-2-2-2-2-22222-222-22-2-200000000-2-22222-2-20000000000000000000000000000
χ412222-2-2-2-2-2-222-2-222222-2-2-2-222-222-2-2000000000000000022-2-2-2-22200000000000000000000
χ422222-2-2-2-2-2-222-2-222222-2-2-2-222-222-2-20000000000000000-2-22222-2-200000000000000000000
χ432222-2-2-2-2-2-222-2-22-2-222-2-2222-22-2-222000000000000000000000000000000000000002i−2i−2i2i00
χ442222-2-2-2-2-2-222-2-22-2-222-2-2222-22-2-22200000000000000000000000000000000000000−2i2i2i−2i00
χ4522-2-222-2-22-22-22-2-2002-22-2002000000002i−2i002i−2ii2−i2i2−i2i2−i2i2−i2000000002−22−22−22−2000000000000
χ4622-2-222-2-22-22-22-2-2002-22-2002000000002i−2i002i−2i−i2i2−i2i2−i2i2−i2i200000000−22−22−22−22000000000000
χ4722-2-222-2-22-22-22-2-2002-22-200200000000−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i200000000−22−22−22−22000000000000
χ4822-2-222-2-22-22-22-2-2002-22-200200000000−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−2000000000000
χ4922-2-222-2-2-22-222-2-200-22-22002000000002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i2000000002−22−2−22−22000000000000
χ5022-2-222-2-2-22-222-2-200-22-22002000000002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i200000000−22−222−22−2000000000000
χ5122-2-222-2-2-22-222-2-200-22-2200200000000−2i2i002i−2ii2−i2i2−i2−i2i2−i2i200000000−22−222−22−2000000000000
χ5222-2-222-2-2-22-222-2-200-22-2200200000000−2i2i002i−2i−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−22000000000000
χ5322-2-2-2-2222-2-222-22002-2-2200-20000002i−2i002i−2i00i2−i2−i2i2i2−i2−i2i2000000002−2−222−2−22000000000000
χ5422-2-2-2-2222-2-222-22002-2-2200-20000002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i200000000−222−2−222−2000000000000
χ5522-2-2-2-2222-2-222-22002-2-2200-2000000−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i200000000−222−2−222−2000000000000
χ5622-2-2-2-2222-2-222-22002-2-2200-2000000−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i2000000002−2−222−2−22000000000000
χ5722-2-2-2-222-222-22-2200-222-200-20000002i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i2000000002−2−22−222−2000000000000
χ5822-2-2-2-222-222-22-2200-222-200-20000002i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i200000000−222−22−2−22000000000000
χ5922-2-2-2-222-222-22-2200-222-200-2000000−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i200000000−222−22−2−22000000000000
χ6022-2-2-2-222-222-22-2200-222-200-2000000−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i2000000002−2−22−222−2000000000000
χ6144-4-444-4-44-44-4-44400-44-4400-400000000000000000000000000000000000000000000000000
χ6244-4-444-4-4-44-44-444004-44-400-400000000000000000000000000000000000000000000000000
χ6344-4-4-4-4444-4-44-44-400-444-400400000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-444-4-44-4004-4-4400400000000000000000000000000000000000000000000000000
χ654-44-44-4-4400000004-400004-4000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ664-44-44-4-4400000004-400004-400000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ674-44-44-4-440000000-440000-440000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ684-44-44-4-440000000-440000-44000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ694-44-4-444-400000004-40000-44000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ704-44-4-444-400000004-40000-4400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ714-44-4-444-40000000-4400004-40000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ724-44-4-444-40000000-4400004-4000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ738-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000

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