Finite Group Databasebeta

← Group #322008

Character table — Group #322008

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444448888888888888888448888888888888888222244444444444488888888888888882222
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11-1-11
χ17222222222-2-222-22-22222222200000000-2-2-2-2-2-2000000000000222200000000-2-2-2-200000000000000000000
χ18222222222-2-222-22-22222222200000000-2-2-2-2-2-2000000000000-2-2-2-200000000222200000000000000000000
χ19222222222-2-222-22-2-2-2-2-2-2-2-2-200000000-2-2222200000000000022-2-200000000-2-22200000000000000000000
χ20222222222-2-222-22-2-2-2-2-2-2-2-2-200000000-2-22222000000000000-2-2220000000022-2-200000000000000000000
χ2122222222-222-2-22-220000000022222222-2-20000-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ2222222222-222-2-22-220000000022222222-2-20000-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ2322222222-222-2-22-2200000000-2-2-2-2-2-2-2-2-2-20000222200000000000022-2-2-2-222000000000000000000000000
χ2422222222-222-2-22-2200000000-2-2-2-2-2-2-2-2-2-200002222000000000000-2-22222-2-2000000000000000000000000
χ252222-2-2-2-22002-20-202222-2-2-2-22222−2−2−2−200000022−2−22222−2−2−2−20000000000002i−2i2i−2i00000000i2i2−i2−i2i2i2−i2−i20000
χ262222-2-2-2-22002-20-202222-2-2-2-22222−2−2−2−200000022−2−22222−2−2−2−2000000000000−2i2i−2i2i00000000−i2−i2i2i2−i2−i2i2i20000
χ272222-2-2-2-22002-20-202222-2-2-2-2−2−2−2−22222000000−2−222−2−2−2−222220000000000002i−2i2i−2i00000000−i2−i2i2i2−i2−i2i2i20000
χ282222-2-2-2-22002-20-202222-2-2-2-2−2−2−2−22222000000−2−222−2−2−2−22222000000000000−2i2i−2i2i00000000i2i2−i2−i2i2i2−i2−i20000
χ292222-2-2-2-22002-20-20-2-2-2-222222222−2−2−2−200000022−2−2−2−2−2−222220000000000002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i20000
χ302222-2-2-2-22002-20-20-2-2-2-222222222−2−2−2−200000022−2−2−2−2−2−22222000000000000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i20000
χ312222-2-2-2-22002-20-20-2-2-2-22222−2−2−2−22222000000−2−2222222−2−2−2−20000000000002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i20000
χ322222-2-2-2-22002-20-20-2-2-2-22222−2−2−2−22222000000−2−2222222−2−2−2−2000000000000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i20000
χ3322-2-2-22-2202-200-20222−2−222−2−222-2-222-2-20022−2−2000022−2−222−2−20000002-2002-2000022−2−222−2−2000000000000
χ3422-2-2-22-2202-200-20222−2−222−2−222-2-222-2-20022−2−2000022−2−222−2−2000000-2200-220000−2−222−2−222000000000000
χ3522-2-2-22-2202-200-20222−2−222−2−2-2-222-2-2220022−2−20000−2−222−2−2220000002-200-22000022−2−2−2−222000000000000
χ3622-2-2-22-2202-200-20222−2−222−2−2-2-222-2-2220022−2−20000−2−222−2−222000000-22002-20000−2−22222−2−2000000000000
χ3722-2-2-22-2202-200-202−2−222−2−22222-2-222-2-200−2−2220000−2−222−2−2220000002-2002-20000−2−222−2−222000000000000
χ3822-2-2-22-2202-200-202−2−222−2−22222-2-222-2-200−2−2220000−2−222−2−222000000-2200-22000022−2−222−2−2000000000000
χ3922-2-2-22-2202-200-202−2−222−2−222-2-222-2-22200−2−222000022−2−222−2−20000002-200-220000−2−22222−2−2000000000000
χ4022-2-2-22-2202-200-202−2−222−2−222-2-222-2-22200−2−222000022−2−222−2−2000000-22002-2000022−2−2−2−222000000000000
χ412-22-2-2-2220-2200-2022−22−22−22−22-22-22-22-2002−22−200002−22−22−22−200002-2002-20000002−22−22−22−2000000000000
χ422-22-2-2-2220-2200-2022−22−22−22−22-22-22-22-2002−22−200002−22−22−22−20000-2200-22000000−22−22−22−22000000000000
χ432-22-2-2-2220-2200-2022−22−22−22−2-22-22-22-22002−22−20000−22−22−22−2200002-200-220000002−22−2−22−22000000000000
χ442-22-2-2-2220-2200-2022−22−22−22−2-22-22-22-22002−22−20000−22−22−22−220000-22002-2000000−22−222−22−2000000000000
χ452-22-2-2-2220-2200-202−22−22−22−222-22-22-22-200−22−220000−22−22−22−2200002-2002-2000000−22−22−22−22000000000000
χ462-22-2-2-2220-2200-202−22−22−22−222-22-22-22-200−22−220000−22−22−22−220000-2200-220000002−22−22−22−2000000000000
χ472-22-2-2-2220-2200-202−22−22−22−22-22-22-22-2200−22−2200002−22−22−22−200002-200-22000000−22−222−22−2000000000000
χ482-22-2-2-2220-2200-202−22−22−22−22-22-22-22-2200−22−2200002−22−22−22−20000-22002-20000002−22−2−22−22000000000000
χ492-2-222-2-222-2-2-2-2222000000002-2-222-2-222-200002-22-20000000000000000000000002-2-222-2-22000000000000
χ502-2-222-2-222-2-2-2-2222000000002-2-222-2-222-200002-22-2000000000000000000000000-222-2-222-2000000000000
χ512-2-222-2-222-2-2-2-222200000000-222-2-222-22-20000-22-220000000000000000000000002-2-22-222-2000000000000
χ522-2-222-2-222-2-2-2-222200000000-222-2-222-22-20000-22-22000000000000000000000000-222-22-2-22000000000000
χ532-2-222-2-22-22222-2-2-22-2-222-2-22000000002-2-222-20000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000
χ542-2-222-2-22-22222-2-2-22-2-222-2-22000000002-2-222-2000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000
χ552-2-222-2-22-22222-2-2-2-222-2-222-2000000002-22-2-220000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000
χ562-2-222-2-22-22222-2-2-2-222-2-222-2000000002-22-2-22000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000
χ572-2-222-2-22-2-2-2222-222-2-222-2-222-2-222-2-22-222-2-22-22-222-2-222-2-22000000000000000000000000000000000000
χ582-2-222-2-22-2-2-2222-222-2-222-2-22-222-2-222-2-222-2-222-22-2-222-2-222-2000000000000000000000000000000000000
χ592-2-222-2-22-2-2-2222-22-222-2-222-22-2-222-2-22-22-222-2-22-22-222-2-222-2000000000000000000000000000000000000
χ602-2-222-2-22-2-2-2222-22-222-2-222-2-222-2-222-2-22-222-22-22-22-2-222-2-22000000000000000000000000000000000000
χ612-2-22-222-2-2002-20202-2-22-222-22−2−22−222−2000000−222−22−2−22−222−22-22-2000000000000000000002−2−222−2−220000
χ622-2-22-222-2-2002-20202-2-22-222-22−2−22−222−2000000−222−22−2−22−222−2-22-2200000000000000000000−222−2−222−20000
χ632-2-22-222-2-2002-20202-2-22-222-2−222−22−2−220000002−2−22−222−22−2−222-22-200000000000000000000−222−2−222−20000
χ642-2-22-222-2-2002-20202-2-22-222-2−222−22−2−220000002−2−22−222−22−2−22-22-22000000000000000000002−2−222−2−220000
χ652-2-22-222-2-2002-2020-222-22-2-222−2−22−222−2000000−222−2−222−22−2−222-2-22000000000000000000002−2−22−222−20000
χ662-2-22-222-2-2002-2020-222-22-2-222−2−22−222−2000000−222−2−222−22−2−22-222-200000000000000000000−222−22−2−220000
χ672-2-22-222-2-2002-2020-222-22-2-22−222−22−2−220000002−2−222−2−22−222−22-2-2200000000000000000000−222−22−2−220000
χ682-2-22-222-2-2002-2020-222-22-2-22−222−22−2−220000002−2−222−2−22−222−2-222-2000000000000000000002−2−22−222−20000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ704444-4-4-4-4-400-440400000000022222222−22−22−22−22000000−22−22222200000000000000000000000000000000000000000000
χ714444-4-4-4-4-400-4404000000000−22−22−22−22222222220000002222−22−2200000000000000000000000000000000000000000000
χ7244-4-44-44-4000000002222−22−22−22−2222222222−22−22−22−222222000000000022-2-2-2-222000000000000000000000000000000000000
χ7344-4-44-44-4000000002222−22−22−22−222222−22−2222222222−22−220000000000-2-22222-2-2000000000000000000000000000000000000
χ7444-4-44-44-400000000−22−2222222222−22−222222−22−22−22−2222220000000000-2-22222-2-2000000000000000000000000000000000000
χ7544-4-44-44-400000000−22−2222222222−22−22−22−2222222222−22−22000000000022-2-2-2-222000000000000000000000000000000000000
χ7644-4-4-44-440-440040-42222−22−222222−22−220000000000−22−222222000000000000000000000000000000000000000000000000
χ7744-4-4-44-440-440040-4−22−222222−22−22222200000000002222−22−22000000000000000000000000000000000000000000000000
χ784-44-444-4-40000000022−2222−22−2222−222222−2222−22−2222−222200000000002-22-2-22-22000000000000000000000000000000000000
χ794-44-444-4-40000000022−2222−22−2222−2222−2222−222222−2222−220000000000-22-222-22-2000000000000000000000000000000000000
χ804-44-444-4-400000000−2222−222222−2222−2222−2222−22−2222−22220000000000-22-222-22-2000000000000000000000000000000000000
χ814-44-444-4-400000000−2222−222222−2222−22−2222−222222−2222−2200000000002-22-2-22-22000000000000000000000000000000000000
χ824-44-4-4-44404-40040-422−2222−2222−2222−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ834-44-4-4-44404-40040-4−2222−2222−2222−2222000000000022−2222−22000000000000000000000000000000000000000000000000
χ844-4-444-4-44444-4-4-44-40000000000000000-440000000000000000000000000000000000000000000000000000
χ854-4-44-444-4400-440-400000000022−22−2222−222222−2200000022−22−222200000000000000000000000000000000000000000000
χ864-4-44-444-4400-440-4000000000−222222−2222−22−2222000000−222222−2200000000000000000000000000000000000000000000

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