Finite Group Databasebeta

← Group #322028

Character table — Group #322028

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444448888888888888888448888888888888888444444444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11-1-11
χ1722222222222-2-2-2-220000000022222222-2-20000-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ1822222222222-2-2-2-220000000022222222-2-20000-2-2-2-200000000-2-222-2-2220000000000000000000000000000
χ1922222222222-2-2-2-2200000000-2-2-2-2-2-2-2-2-2-2000022220000000022-2-2-2-2220000000000000000000000000000
χ2022222222222-2-2-2-2200000000-2-2-2-2-2-2-2-2-2-20000222200000000-2-22222-2-20000000000000000000000000000
χ2122222222-2-2-22222-22222222200000000-2-2-2-2-2-20000000000000000000022-2-222-2-200000000000000000000
χ2222222222-2-2-22222-22222222200000000-2-2-2-2-2-200000000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000022-2-2-2-22200000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-200000000-2-2222200000000000000000000-2-22222-2-200000000000000000000
χ252222-2-2-2-22-220000-22222−2−2−2−22222-2-2-2-20022−2−200002222−2−2−2−2002-2002-20000000022−2−222−2−2000000000000
χ262222-2-2-2-22-220000-22222−2−2−2−22222-2-2-2-20022−2−200002222−2−2−2−200-2200-2200000000−2−222−2−222000000000000
χ272222-2-2-2-22-220000-22222−2−2−2−2-2-2-2-222220022−2−20000−2−2−2−22222002-200-220000000022−2−2−2−222000000000000
χ282222-2-2-2-22-220000-22222−2−2−2−2-2-2-2-222220022−2−20000−2−2−2−2222200-22002-200000000−2−22222−2−2000000000000
χ292222-2-2-2-22-220000-2−2−2−2−222222222-2-2-2-200−2−2220000−2−2−2−22222002-2002-200000000−2−222−2−222000000000000
χ302222-2-2-2-22-220000-2−2−2−2−222222222-2-2-2-200−2−2220000−2−2−2−2222200-2200-220000000022−2−222−2−2000000000000
χ312222-2-2-2-22-220000-2−2−2−2−22222-2-2-2-2222200−2−22200002222−2−2−2−2002-200-2200000000−2−22222−2−2000000000000
χ322222-2-2-2-22-220000-2−2−2−2−22222-2-2-2-2222200−2−22200002222−2−2−2−200-22002-20000000022−2−2−2−222000000000000
χ3322-2-222-2-2-2220000-222−2−222−2−222-2-222-2-2002−22−2000022−2−222−2−22-2002-200000000002−22−22−22−2000000000000
χ3422-2-222-2-2-2220000-222−2−222−2−222-2-222-2-2002−22−2000022−2−222−2−2-2200-220000000000−22−22−22−22000000000000
χ3522-2-222-2-2-2220000-222−2−222−2−2-2-222-2-222002−22−20000−2−222−2−2222-200-2200000000002−22−2−22−22000000000000
χ3622-2-222-2-2-2220000-222−2−222−2−2-2-222-2-222002−22−20000−2−222−2−222-22002-20000000000−22−222−22−2000000000000
χ3722-2-222-2-2-2220000-2−2−222−2−22222-2-222-2-200−22−220000−2−222−2−2222-2002-20000000000−22−22−22−22000000000000
χ3822-2-222-2-2-2220000-2−2−222−2−22222-2-222-2-200−22−220000−2−222−2−222-2200-2200000000002−22−22−22−2000000000000
χ3922-2-222-2-2-2220000-2−2−222−2−222-2-222-2-22200−22−22000022−2−222−2−22-200-220000000000−22−222−22−2000000000000
χ4022-2-222-2-2-2220000-2−2−222−2−222-2-222-2-22200−22−22000022−2−222−2−2-22002-200000000002−22−2−22−22000000000000
χ4122-2-2-2-22222-222-2-2-222-2-2-2-222000000002-2-222-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ4222-2-2-2-22222-222-2-2-222-2-2-2-222000000002-2-222-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ4322-2-2-2-22222-222-2-2-2-2-22222-2-2000000002-22-2-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000
χ4422-2-2-2-22222-222-2-2-2-2-22222-2-2000000002-22-2-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000
χ4522-2-2-2-222-2-2222-2-2222-2-2-2-22222-2-2-2-222-222-2-2222-2-222-2-2-2-222000000000000000000000000000000000000
χ4622-2-2-2-222-2-2222-2-2222-2-2-2-222-2-22222-2-2-222-2-22-2-222-2-22222-2-2000000000000000000000000000000000000
χ4722-2-2-2-222-2-2222-2-22-2-22222-2-222-2-2-2-222-22-222-222-2-2-2-22222-2-2000000000000000000000000000000000000
χ4822-2-2-2-222-2-2222-2-22-2-22222-2-2-2-22222-2-2-22-222-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ4922-2-2-2-222-2-22-2-22220000000022-2-2-2-2222-20000-2-2220000000000000000000000002-2-222-2-22000000000000
χ5022-2-2-2-222-2-22-2-22220000000022-2-2-2-2222-20000-2-222000000000000000000000000-222-2-222-2000000000000
χ5122-2-2-2-222-2-22-2-222200000000-2-22222-2-22-2000022-2-20000000000000000000000002-2-22-222-2000000000000
χ5222-2-2-2-222-2-22-2-222200000000-2-22222-2-22-2000022-2-2000000000000000000000000-222-22-2-22000000000000
χ532-22-22-22-20002-22-202i−2i2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i22−22−22−22−200000000002i−2i002-2000000002−22−2i2−i2i2−i20000
χ542-22-22-22-20002-22-202i−2i2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i22−22−22−22−20000000000−2i2i00-2200000000−22−22−i2i2−i2i20000
χ552-22-22-22-20002-22-202i−2i2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2−22−22−22−2200000000002i−2i002-200000000−22−22−i2i2−i2i20000
χ562-22-22-22-20002-22-202i−2i2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2−22−22−22−220000000000−2i2i00-22000000002−22−2i2−i2i2−i20000
χ572-22-22-22-20002-22-20−2i2i−2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2−22−22−22−2200000000002i−2i00-22000000002−22−2−i2i2−i2i20000
χ582-22-22-22-20002-22-20−2i2i−2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2−22−22−22−220000000000−2i2i002-200000000−22−22i2−i2i2−i20000
χ592-22-22-22-20002-22-20−2i2i−2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i22−22−22−22−200000000002i−2i00-2200000000−22−22i2−i2i2−i20000
χ602-22-22-22-20002-22-20−2i2i−2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i22−22−22−22−20000000000−2i2i002-2000000002−22−2−i2i2−i2i20000
χ612-2-22-222-20002-2-2202i−2i−2i2i−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2000000i2−i2−i2i22−2−22−222−2000000002-2002i−2i0000000000i2−i2−i2i2−222−20000
χ622-2-22-222-20002-2-2202i−2i−2i2i−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2000000i2−i2−i2i22−2−22−222−200000000-2200−2i2i0000000000−i2i2i2−i22−2−220000
χ632-2-22-222-20002-2-2202i−2i−2i2i−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2000000−i2i2i2−i2−222−22−2−22000000002-2002i−2i0000000000−i2i2i2−i22−2−220000
χ642-2-22-222-20002-2-2202i−2i−2i2i−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2000000−i2i2i2−i2−222−22−2−2200000000-2200−2i2i0000000000i2−i2−i2i2−222−20000
χ652-2-22-222-20002-2-220−2i2i2i−2i2i−2i−2i2ii2−i2−i2i2−i2i2i2−i2000000i2−i2−i2i2−222−22−2−22000000002-200−2i2i0000000000i2−i2−i2i22−2−220000
χ662-2-22-222-20002-2-220−2i2i2i−2i2i−2i−2i2ii2−i2−i2i2−i2i2i2−i2000000i2−i2−i2i2−222−22−2−2200000000-22002i−2i0000000000−i2i2i2−i2−222−20000
χ672-2-22-222-20002-2-220−2i2i2i−2i2i−2i−2i2i−i2i2i2−i2i2−i2−i2i2000000−i2i2i2−i22−2−22−222−2000000002-200−2i2i0000000000−i2i2i2−i2−222−20000
χ682-2-22-222-20002-2-220−2i2i2i−2i2i−2i−2i2i−i2i2i2−i2i2−i2−i2i2000000−i2i2i2−i22−2−22−222−200000000-22002i−2i0000000000i2−i2−i2i22−2−220000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ704444-4-4-4-4-44-40000422222222−22−22−22−220000000000−22−222222000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-44-400004−22−22−22−222222222200000000002222−22−22000000000000000000000000000000000000000000000000
χ7244-4-444-4-44-4-4000042222−22−222222−22−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ7344-4-444-4-44-4-400004−22−222222−22−222222000000000022−2222−22000000000000000000000000000000000000000000000000
χ7444-4-4-4-44444-4-4-444-40000000000000000-440000000000000000000000000000000000000000000000000000
χ754-44-44-44-4000-44-440000000002i2−2i22i2−2i22i2−2i22i2−2i2000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ764-44-44-44-4000-44-44000000000−2i22i2−2i22i2−2i22i2−2i22i20000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ774-44-4-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i200000000002-22-2-22-22000000000000000000000000000000000000
χ784-44-4-44-44000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000-22-222-22-2000000000000000000000000000000000000
χ794-44-4-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000-22-222-22-2000000000000000000000000000000000000
χ804-44-4-44-4400000000−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i200000000002-22-2-22-22000000000000000000000000000000000000
χ814-4-444-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i200000000002-2-222-2-22000000000000000000000000000000000000
χ824-4-444-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i20000000000-222-2-222-2000000000000000000000000000000000000
χ834-4-444-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i20000000000-222-2-222-2000000000000000000000000000000000000
χ844-4-444-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i200000000002-2-222-2-22000000000000000000000000000000000000
χ854-4-44-444-4000-444-40000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ864-4-44-444-4000-444-4000000000−2i22i22i2−2i22i2−2i2−2i22i20000002i2−2i2−2i22i200000000000000000000000000000000000000000000

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