Finite Group Databasebeta

← Group #288754

Character table — Group #288754

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444448888888888888888448888888888888888444444444444444488888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111111-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-111-1
χ172222222222-22-2-2-220000000022222222-2-20000-2-2-2-2000000002222-2-20000-2-2000000000000000000000000
χ182222222222-22-2-2-220000000022222222-2-20000-2-2-2-200000000-2-2-2-222000022000000000000000000000000
χ192222222222-22-2-2-2200000000-2-2-2-2-2-2-2-2-2-2000022220000000022-2-2-2-2000022000000000000000000000000
χ202222222222-22-2-2-2200000000-2-2-2-2-2-2-2-2-2-20000222200000000-2-222220000-2-2000000000000000000000000
χ2122222222-2-22-2222-22222222200000000-2-2-2-2-2-200000000000000000022-2-200-2-22200000000000000000000
χ2222222222-2-22-2222-22222222200000000-2-2-2-2-2-2000000000000000000-2-2220022-2-200000000000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000222200-2-2-2-200000000000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000-2-2-2-200222200000000000000000000
χ252222-2-2-2-22-202000-22222−2−2−2−22222-2-2-2-20022−2−200002222−2−2−2−22-22-200000000000022−2−222−2−2000000000000
χ262222-2-2-2-22-202000-22222−2−2−2−22222-2-2-2-20022−2−200002222−2−2−2−2-22-22000000000000−2−222−2−222000000000000
χ272222-2-2-2-22-202000-22222−2−2−2−2-2-2-2-222220022−2−20000−2−2−2−222222-2-2200000000000022−2−2−2−222000000000000
χ282222-2-2-2-22-202000-22222−2−2−2−2-2-2-2-222220022−2−20000−2−2−2−22222-222-2000000000000−2−22222−2−2000000000000
χ292222-2-2-2-22-202000-2−2−2−2−222222222-2-2-2-200−2−2220000−2−2−2−222222-22-2000000000000−2−222−2−222000000000000
χ302222-2-2-2-22-202000-2−2−2−2−222222222-2-2-2-200−2−2220000−2−2−2−22222-22-2200000000000022−2−222−2−2000000000000
χ312222-2-2-2-22-202000-2−2−2−2−22222-2-2-2-2222200−2−22200002222−2−2−2−22-2-22000000000000−2−22222−2−2000000000000
χ322222-2-2-2-22-202000-2−2−2−2−22222-2-2-2-2222200−2−22200002222−2−2−2−2-222-200000000000022−2−2−2−222000000000000
χ3322-2-22-22-200-20-22202i2i−2i−2i2i2i−2i−2i22−2−222−2−200000022−2−2i2i2−i2−i2i2i2−i2−i2000000002-2002i−2i0000000000i2i2−i2−i222−2−20000
χ3422-2-22-22-200-20-22202i2i−2i−2i2i2i−2i−2i22−2−222−2−200000022−2−2i2i2−i2−i2i2i2−i2−i200000000-2200−2i2i0000000000−i2−i2i2i2−2−2220000
χ3522-2-22-22-200-20-22202i2i−2i−2i2i2i−2i−2i−2−222−2−222000000−2−222−i2−i2i2i2−i2−i2i2i2000000002-2002i−2i0000000000−i2−i2i2i2−2−2220000
χ3622-2-22-22-200-20-22202i2i−2i−2i2i2i−2i−2i−2−222−2−222000000−2−222−i2−i2i2i2−i2−i2i2i200000000-2200−2i2i0000000000i2i2−i2−i222−2−20000
χ3722-2-22-22-200-20-2220−2i−2i2i2i−2i−2i2i2i22−2−222−2−200000022−2−2−i2−i2i2i2−i2−i2i2i2000000002-200−2i2i0000000000−i2−i2i2i222−2−20000
χ3822-2-22-22-200-20-2220−2i−2i2i2i−2i−2i2i2i22−2−222−2−200000022−2−2−i2−i2i2i2−i2−i2i2i200000000-22002i−2i0000000000i2i2−i2−i2−2−2220000
χ3922-2-22-22-200-20-2220−2i−2i2i2i−2i−2i2i2i−2−222−2−222000000−2−222i2i2−i2−i2i2i2−i2−i2000000002-200−2i2i0000000000i2i2−i2−i2−2−2220000
χ4022-2-22-22-200-20-2220−2i−2i2i2i−2i−2i2i2i−2−222−2−222000000−2−222i2i2−i2−i2i2i2−i2−i200000000-22002i−2i0000000000−i2−i2i2i222−2−20000
χ412-22-2-222-20020-2-2202i−2i2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i22−22−22−22−20000002-20000002i−2i00000000i2−i2i2−i22−22−20000
χ422-22-2-222-20020-2-2202i−2i2i−2i2i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i22−22−22−22−2000000-22000000−2i2i00000000−i2i2−i2i2−22−220000
χ432-22-2-222-20020-2-2202i−2i2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2−22−22−22−220000002-20000002i−2i00000000−i2i2−i2i2−22−220000
χ442-22-2-222-20020-2-2202i−2i2i−2i2i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2−22−22−22−22000000-22000000−2i2i00000000i2−i2i2−i22−22−20000
χ452-22-2-222-20020-2-220−2i2i−2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2−22−22−22−220000002-2000000−2i2i00000000i2−i2i2−i2−22−220000
χ462-22-2-222-20020-2-220−2i2i−2i2i−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2−22−22−22−22000000-220000002i−2i00000000−i2i2−i2i22−22−20000
χ472-22-2-222-20020-2-220−2i2i−2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i22−22−22−22−20000002-2000000−2i2i00000000−i2i2−i2i22−22−20000
χ482-22-2-222-20020-2-220−2i2i−2i2i−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i22−22−22−22−2000000-220000002i−2i00000000i2−i2i2−i2−22−220000
χ492-2-2222-2-22-20-200022−2−22−222−22i−2i−2i2i−2i2i2i−2i002−22−20000−i2i2i2−i2i2−i2−i2i200002-200002i−2i00002−22−2i2−i2i2−i2000000000000
χ502-2-2222-2-22-20-200022−2−22−222−22i−2i−2i2i−2i2i2i−2i002−22−20000−i2i2i2−i2i2−i2−i2i20000-220000−2i2i0000−22−22−i2i2−i2i2000000000000
χ512-2-2222-2-22-20-200022−2−22−222−2−2i2i2i−2i2i−2i−2i2i002−22−20000i2−i2−i2i2−i2i2i2−i200002-20000−2i2i00002−22−2−i2i2−i2i2000000000000
χ522-2-2222-2-22-20-200022−2−22−222−2−2i2i2i−2i2i−2i−2i2i002−22−20000i2−i2−i2i2−i2i2i2−i20000-2200002i−2i0000−22−22i2−i2i2−i2000000000000
χ532-2-2222-2-22-20-20002−222−22−2−222i−2i−2i2i−2i2i2i−2i00−22−220000i2−i2−i2i2−i2i2i2−i200002-200002i−2i0000−22−22−i2i2−i2i2000000000000
χ542-2-2222-2-22-20-20002−222−22−2−222i−2i−2i2i−2i2i2i−2i00−22−220000i2−i2−i2i2−i2i2i2−i20000-220000−2i2i00002−22−2i2−i2i2−i2000000000000
χ552-2-2222-2-22-20-20002−222−22−2−22−2i2i2i−2i2i−2i−2i2i00−22−220000−i2i2i2−i2i2−i2−i2i200002-20000−2i2i0000−22−22i2−i2i2−i2000000000000
χ562-2-2222-2-22-20-20002−222−22−2−22−2i2i2i−2i2i−2i−2i2i00−22−220000−i2i2i2−i2i2−i2−i2i20000-2200002i−2i00002−22−2−i2i2−i2i2000000000000
χ572-2-22-2-222222-2-22-2-2000000002i−2i−2i2i2i−2i−2i2i-220000−2i2i2i−2i0000000000000000000000002-2-222i−2i−2i2i000000000000
χ582-2-22-2-222222-2-22-2-2000000002i−2i−2i2i2i−2i−2i2i-220000−2i2i2i−2i000000000000000000000000-222-2−2i2i2i−2i000000000000
χ592-2-22-2-222222-2-22-2-200000000−2i2i2i−2i−2i2i2i−2i-2200002i−2i−2i2i0000000000000000000000002-2-22−2i2i2i−2i000000000000
χ602-2-22-2-222222-2-22-2-200000000−2i2i2i−2i−2i2i2i−2i-2200002i−2i−2i2i000000000000000000000000-222-22i−2i−2i2i000000000000
χ612-2-22-2-22222-2-22-22-22-2-222-2-222i−2i−2i2i2i−2i−2i2i2-22-2-222i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ622-2-22-2-22222-2-22-22-22-2-222-2-22−2i2i2i−2i−2i2i2i−2i2-22-2-22−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ632-2-22-2-22222-2-22-22-2-222-2-222-22i−2i−2i2i2i−2i−2i2i2-2-222-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ642-2-22-2-22222-2-22-22-2-222-2-222-2−2i2i2i−2i−2i2i2i−2i2-2-222-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ652-2-22-2-222-2-2-222-2222-2-222-2-2200000000-22-222-20000000000000000000000000000000000002-2-222-2-220000
χ662-2-22-2-222-2-2-222-2222-2-222-2-2200000000-22-222-2000000000000000000000000000000000000-222-2-222-20000
χ672-2-22-2-222-2-2-222-222-222-2-222-200000000-222-2-220000000000000000000000000000000000002-2-22-222-20000
χ682-2-22-2-222-2-2-222-222-222-2-222-200000000-222-2-22000000000000000000000000000000000000-222-22-2-220000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ704444-4-4-4-4-440-4000422222222−22−22−22−220000000000−22−222222000000000000000000000000000000000000000000000000
χ714444-4-4-4-4-440-40004−22−22−22−222222222200000000002222−22−22000000000000000000000000000000000000000000000000
χ7244-4-44-44-400404-4-40000000002222−22−222222−22−22000000−22−22222200000000000000000000000000000000000000000000
χ7344-4-44-44-400404-4-4000000000−22−222222−22−2222220000002222−22−2200000000000000000000000000000000000000000000
χ7444-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i22222−22−22−22−22222200000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ7544-4-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i2−22−2222222222−22−220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ7644-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i22222−22−22−22−2222220000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ7744-4-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i2−22−2222222222−22−2200000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ784-44-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i200000000002-22-2-22-22000000000000000000000000000000000000
χ794-44-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000-22-222-22-2000000000000000000000000000000000000
χ804-44-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000-22-222-22-2000000000000000000000000000000000000
χ814-44-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i200000000002-22-2-22-22000000000000000000000000000000000000
χ824-44-4-444-400-4044-40000000002i2−2i22i2−2i22i2−2i22i2−2i2000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ834-44-4-444-400-4044-4000000000−2i22i2−2i22i2−2i22i2−2i22i20000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ844-4-4444-4-4-4404000-422−22−2222−222222−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ854-4-4444-4-4-4404000-4−222222−2222−22−2222000000000022−2222−22000000000000000000000000000000000000000000000000
χ864-4-44-4-444-4-444-44-4400000000000000004-40000000000000000000000000000000000000000000000000000

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