Finite Group Databasebeta

← Group #300076

Character table — Group #300076

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order12222244444444224444888888884444448888888888888888444444442288
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-1
χ911111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1
χ1011111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-11-1-11
χ17222222222-2-2-2-222222-2-200000000-2-222-2-222-2-2000000000000000000000000
χ18222222222-2-2-2-222222-2-200000000-2-2-2-222-2-222000000000000000000000000
χ19222222222-2-2-2-22-2-2-2-2-2-2000000002222-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-22-2-2-2-2-2-20000000022-2-22222-2-2000000000000000000000000
χ21222222-2-2-2-2-222-20000-222222-2-2-2-200000000000000000000002-2002-2000000
χ22222222-2-2-2-2-222-20000-222222-2-2-2-20000000000000000000000-2200-22000000
χ23222222-2-2-2-2-222-20000-22-2-2-2-2222200000000000000000000002-200-22000000
χ24222222-2-2-2-2-222-20000-22-2-2-2-222220000000000000000000000-22002-2000000
χ252222-2-22-2-222-2-2222-2-2-22000000002-20000000022-2-2000022-2-2000000000000
χ262222-2-22-2-222-2-2222-2-2-22000000002-200000000-2-2220000-2-222000000000000
χ272222-2-22-2-222-2-22-2-222-2200000000-220000000022-2-20000-2-222000000000000
χ282222-2-22-2-222-2-22-2-222-2200000000-2200000000-2-222000022-2-2000000000000
χ292222-2-22-2-2-2-222222-2-22-222-2-222-2-2-2200000000000022-2-20000000000000000
χ302222-2-22-2-2-2-222222-2-22-2-2-222-2-222-22000000000000-2-2220000000000000000
χ312222-2-22-2-2-2-2222-2-2222-222-2-222-2-22-2000000000000-2-2220000000000000000
χ322222-2-22-2-2-2-2222-2-2222-2-2-222-2-2222-200000000000022-2-20000000000000000
χ332222-2-2-2222222-20000-2-222-2-2-2-2220000000000000000000000002-2002-20000
χ342222-2-2-2222222-20000-2-222-2-2-2-222000000000000000000000000-2200-220000
χ352222-2-2-2222222-20000-2-2-2-22222-2-20000000000000000000000002-200-220000
χ362222-2-2-2222222-20000-2-2-2-22222-2-2000000000000000000000000-22002-20000
χ3722-2-22-2-22-2000022-22-2002−22−22−22−200002i−2i002i−2ii2−i2i2−i22−22−2i2−i2i2−i2000000000000
χ3822-2-22-2-22-2000022-22-2002−22−22−22−20000−2i2i00−2i2i−i2i2−i2i22−22−2−i2i2−i2i2000000000000
χ3922-2-22-2-22-2000022-22-200−22−22−22−2200002i−2i002i−2i−i2i2−i2i2−22−22−i2i2−i2i2000000000000
χ4022-2-22-2-22-2000022-22-200−22−22−22−220000−2i2i00−2i2ii2−i2i2−i2−22−22i2−i2i2−i2000000000000
χ4122-2-22-2-22-200002-22-22002−22−22−22−200002i−2i00−2i2i−i2i2−i2i2−22−22i2−i2i2−i2000000000000
χ4222-2-22-2-22-200002-22-22002−22−22−22−20000−2i2i002i−2ii2−i2i2−i2−22−22−i2i2−i2i2000000000000
χ4322-2-22-2-22-200002-22-2200−22−22−22−2200002i−2i00−2i2ii2−i2i2−i22−22−2−i2i2−i2i2000000000000
χ4422-2-22-2-22-200002-22-2200−22−22−22−220000−2i2i002i−2i−i2i2−i2i22−22−2i2−i2i2−i2000000000000
χ4522-2-2-22-2-22000022-2-22002−2−222−2−22002i−2i002i−2i00i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ4622-2-2-22-2-22000022-2-22002−2−222−2−2200−2i2i00−2i2i00−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ4722-2-2-22-2-22000022-2-2200−222−2−222−2002i−2i002i−2i00−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ4822-2-2-22-2-22000022-2-2200−222−2−222−200−2i2i00−2i2i00i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ4922-2-2-22-2-2200002-222-2002−2−222−2−22002i−2i00−2i2i00−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ5022-2-2-22-2-2200002-222-2002−2−222−2−2200−2i2i002i−2i00i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ5122-2-2-22-2-2200002-222-200−222−2−222−2002i−2i00−2i2i00i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ5222-2-2-22-2-2200002-222-200−222−2−222−200−2i2i002i−2i00−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ53444444-4-4-444-4-4-400004-4000000000000000000000000000000000000000000
χ544444-4-4-444-4-4-4-4-4000044000000000000000000000000000000000000000000
χ5544-4-44-44-440000-400000022−2222−22−2222−22220000000000000000000000000000000000
χ5644-4-44-44-440000-4000000−2222−222222−2222−220000000000000000000000000000000000
χ5744-4-4-4444-40000-400000022−22−2222−222222−220000000000000000000000000000000000
χ5844-4-4-4444-40000-4000000−222222−2222−22−22220000000000000000000000000000000000
χ598-88-800000008-80000000000000000000000000000000000000000000000000
χ608-88-80000000-880000000000000000000000000000000000000000000000000
χ618-8-88000008-8000000000000000000000000000000000000000000000000000
χ628-8-8800000-88000000000000000000000000000000000000000000000000000

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