Finite Group Databasebeta

← Group #322033

Character table — Group #322033

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order12222222444444448888888888888888448888888888888888444444444444444488888888888888882244
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-111-1
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-11
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ172222222222-2-22-2-220000000022222222-2-20000-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ182222222222-2-22-2-220000000022222222-2-20000-2-2-2-200000000-2-222-2-2220000000000000000000000000000
χ192222222222-2-22-2-2200000000-2-2-2-2-2-2-2-2-2-2000022220000000022-2-2-2-2220000000000000000000000000000
χ202222222222-2-22-2-2200000000-2-2-2-2-2-2-2-2-2-20000222200000000-2-22222-2-20000000000000000000000000000
χ2122222222-2-222-222-22222222200000000-2-2-2-2-2-20000000000000000000022-2-222-2-200000000000000000000
χ2222222222-2-222-222-22222222200000000-2-2-2-2-2-200000000000000000000-2-222-2-22200000000000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000022-2-2-2-22200000000000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2-2-200000000-2-2222200000000000000000000-2-22222-2-200000000000000000000
χ25222-2-22-2-2002-202-202i2i2i2i−2i−2i−2i−2ii2i2i2i2−i2−i2−i2−i2000000i2i2−i2−i22222−2−2−2−200000000002-2002i−2i00000000i2i2−i2−i222−2−20000
χ26222-2-22-2-2002-202-202i2i2i2i−2i−2i−2i−2ii2i2i2i2−i2−i2−i2−i2000000i2i2−i2−i22222−2−2−2−20000000000-2200−2i2i00000000−i2−i2i2i2−2−2220000
χ27222-2-22-2-2002-202-202i2i2i2i−2i−2i−2i−2i−i2−i2−i2−i2i2i2i2i2000000−i2−i2i2i2−2−2−2−2222200000000002-2002i−2i00000000−i2−i2i2i2−2−2220000
χ28222-2-22-2-2002-202-202i2i2i2i−2i−2i−2i−2i−i2−i2−i2−i2i2i2i2i2000000−i2−i2i2i2−2−2−2−222220000000000-2200−2i2i00000000i2i2−i2−i222−2−20000
χ29222-2-22-2-2002-202-20−2i−2i−2i−2i2i2i2i2ii2i2i2i2−i2−i2−i2−i2000000i2i2−i2−i2−2−2−2−2222200000000002-200−2i2i00000000i2i2−i2−i2−2−2220000
χ30222-2-22-2-2002-202-20−2i−2i−2i−2i2i2i2i2ii2i2i2i2−i2−i2−i2−i2000000i2i2−i2−i2−2−2−2−222220000000000-22002i−2i00000000−i2−i2i2i222−2−20000
χ31222-2-22-2-2002-202-20−2i−2i−2i−2i2i2i2i2i−i2−i2−i2−i2i2i2i2i2000000−i2−i2i2i22222−2−2−2−200000000002-200−2i2i00000000−i2−i2i2i222−2−20000
χ32222-2-22-2-2002-202-20−2i−2i−2i−2i2i2i2i2i−i2−i2−i2−i2i2i2i2i2000000−i2−i2i2i22222−2−2−2−20000000000-22002i−2i00000000i2i2−i2−i2−2−2220000
χ3322-22-2-2-222-200200-222−2−222−2−222-2-222-2-20022−2−2000022−2−222−2−2002i−2i002i−2i00000000i2i2−i2−i2i2i2−i2−i2000000000000
χ3422-22-2-2-222-200200-222−2−222−2−222-2-222-2-20022−2−2000022−2−222−2−200−2i2i00−2i2i00000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3522-22-2-2-222-200200-222−2−222−2−2-2-222-2-2220022−2−20000−2−222−2−222002i−2i00−2i2i00000000i2i2−i2−i2−i2−i2i2i2000000000000
χ3622-22-2-2-222-200200-222−2−222−2−2-2-222-2-2220022−2−20000−2−222−2−22200−2i2i002i−2i00000000−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-22-2-2-222-200200-2−2−222−2−22222-2-222-2-200−2−2220000−2−222−2−222002i−2i002i−2i00000000−i2−i2i2i2−i2−i2i2i2000000000000
χ3822-22-2-2-222-200200-2−2−222−2−22222-2-222-2-200−2−2220000−2−222−2−22200−2i2i00−2i2i00000000i2i2−i2−i2i2i2−i2−i2000000000000
χ3922-22-2-2-222-200200-2−2−222−2−222-2-222-2-22200−2−222000022−2−222−2−2002i−2i00−2i2i00000000−i2−i2i2i2i2i2−i2−i2000000000000
χ4022-22-2-2-222-200200-2−2−222−2−222-2-222-2-22200−2−222000022−2−222−2−200−2i2i002i−2i00000000i2i2−i2−i2−i2−i2i2i2000000000000
χ412-22-22-2-22-2200200-22−22−22−22−22-22-22-22-2002−22−200002−22−22−22−22i−2i002i−2i0000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ422-22-22-2-22-2200200-22−22−22−22−22-22-22-22-2002−22−200002−22−22−22−2−2i2i00−2i2i0000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ432-22-22-2-22-2200200-22−22−22−22−2-22-22-22-22002−22−20000−22−22−22−222i−2i00−2i2i0000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ442-22-22-2-22-2200200-22−22−22−22−2-22-22-22-22002−22−20000−22−22−22−22−2i2i002i−2i0000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ452-22-22-2-22-2200200-2−22−22−22−222-22-22-22-200−22−220000−22−22−22−222i−2i002i−2i0000000000−i2i2−i2i2−i2i2−i2i2000000000000
χ462-22-22-2-22-2200200-2−22−22−22−222-22-22-22-200−22−220000−22−22−22−22−2i2i00−2i2i0000000000i2−i2i2−i2i2−i2i2−i2000000000000
χ472-22-22-2-22-2200200-2−22−22−22−22-22-22-22-2200−22−2200002−22−22−22−22i−2i00−2i2i0000000000−i2i2−i2i2i2−i2i2−i2000000000000
χ482-22-22-2-22-2200200-2−22−22−22−22-22-22-22-2200−22−2200002−22−22−22−2−2i2i002i−2i0000000000i2−i2i2−i2−i2i2−i2i2000000000000
χ492-2-2222-2-2002-20-2202i−2i−2i2i−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2000000i2−i2i2−i22−2−22−222−2000000002i−2i002-200000000002−22−2i2−i2i2−i20000
χ502-2-2222-2-2002-20-2202i−2i−2i2i−2i2i2i−2ii2−i2−i2i2−i2i2i2−i2000000i2−i2i2−i22−2−22−222−200000000−2i2i00-220000000000−22−22−i2i2−i2i20000
χ512-2-2222-2-2002-20-2202i−2i−2i2i−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2000000−i2i2−i2i2−222−22−2−22000000002i−2i002-20000000000−22−22−i2i2−i2i20000
χ522-2-2222-2-2002-20-2202i−2i−2i2i−2i2i2i−2i−i2i2i2−i2i2−i2−i2i2000000−i2i2−i2i2−222−22−2−2200000000−2i2i00-2200000000002−22−2i2−i2i2−i20000
χ532-2-2222-2-2002-20-220−2i2i2i−2i2i−2i−2i2ii2−i2−i2i2−i2i2i2−i2000000i2−i2i2−i2−222−22−2−22000000002i−2i00-2200000000002−22−2−i2i2−i2i20000
χ542-2-2222-2-2002-20-220−2i2i2i−2i2i−2i−2i2ii2−i2−i2i2−i2i2i2−i2000000i2−i2i2−i2−222−22−2−2200000000−2i2i002-20000000000−22−22i2−i2i2−i20000
χ552-2-2222-2-2002-20-220−2i2i2i−2i2i−2i−2i2i−i2i2i2−i2i2−i2−i2i2000000−i2i2−i2i22−2−22−222−2000000002i−2i00-220000000000−22−22i2−i2i2−i20000
χ562-2-2222-2-2002-20-220−2i2i2i−2i2i−2i−2i2i−i2i2i2−i2i2−i2−i2i2000000−i2i2−i2i22−2−22−222−200000000−2i2i002-200000000002−22−2−i2i2−i2i20000
χ572-2-2-2-22222222-2-2-2-22-2-222-2-22000000002-2-222-20000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000
χ582-2-2-2-22222222-2-2-2-22-2-222-2-22000000002-2-222-2000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000
χ592-2-2-2-22222222-2-2-2-2-222-2-222-2000000002-22-2-220000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000
χ602-2-2-2-22222222-2-2-2-2-222-2-222-2000000002-22-2-22000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000
χ612-2-2-2-2222-2-2222-2-222-2-222-2-222-2-222-2-22-222-2-222-2-222-2-222-2-22000000000000000000000000000000000000
χ622-2-2-2-2222-2-2222-2-222-2-222-2-22-222-2-222-2-222-2-22-222-2-222-2-222-2000000000000000000000000000000000000
χ632-2-2-2-2222-2-2222-2-22-222-2-222-22-2-222-2-22-22-222-22-2-22-222-2-222-2000000000000000000000000000000000000
χ642-2-2-2-2222-2-2222-2-22-222-2-222-2-222-2-222-2-22-222-2-222-22-2-222-2-22000000000000000000000000000000000000
χ652-2-2-2-2222-2-2-2-22222000000002-2-222-2-222-20000-222-20000000000000000000000002-2-222-2-22000000000000
χ662-2-2-2-2222-2-2-2-22222000000002-2-222-2-222-20000-222-2000000000000000000000000-222-2-222-2000000000000
χ672-2-2-2-2222-2-2-2-2222200000000-222-2-222-22-200002-2-220000000000000000000000002-2-22-222-2000000000000
χ682-2-2-2-2222-2-2-2-2222200000000-222-2-222-22-200002-2-22000000000000000000000000-222-22-2-22000000000000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ70444-4-44-4-400-440-440000000002i22i22i22i2−2i2−2i2−2i2−2i2000000−2i2−2i22i22i200000000000000000000000000000000000000000000
χ71444-4-44-4-400-440-44000000000−2i2−2i2−2i2−2i22i22i22i22i20000002i22i2−2i2−2i200000000000000000000000000000000000000000000
χ7244-44-4-4-44-4400-40042222−22−222222−22−220000000000−22−222222000000000000000000000000000000000000000000000000
χ7344-44-4-4-44-4400-4004−22−222222−22−22222200000000002222−22−22000000000000000000000000000000000000000000000000
χ7444-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i22i22i2−2i2−2i2−2i2−2i22i22i2000000000022-2-2-2-222000000000000000000000000000000000000
χ7544-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i2−2i2−2i22i22i22i22i2−2i2−2i20000000000-2-22222-2-2000000000000000000000000000000000000
χ7644-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i22i22i2−2i2−2i2−2i2−2i22i22i20000000000-2-22222-2-2000000000000000000000000000000000000
χ7744-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i2−2i2−2i22i22i22i22i2−2i2−2i2000000000022-2-2-2-222000000000000000000000000000000000000
χ784-444-4-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i200000000002-22-2-22-22000000000000000000000000000000000000
χ794-444-4-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000-22-222-22-2000000000000000000000000000000000000
χ804-444-4-44-400000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000-22-222-22-2000000000000000000000000000000000000
χ814-444-4-44-400000000−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i200000000002-22-2-22-22000000000000000000000000000000000000
χ824-44-44-4-444-400-400422−2222−2222−2222−220000000000−2222−2222000000000000000000000000000000000000000000000000
χ834-44-44-4-444-400-4004−2222−2222−2222−2222000000000022−2222−22000000000000000000000000000000000000000000000000
χ844-4-4444-4-400-4404-40000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ854-4-4444-4-400-4404-4000000000−2i22i22i2−2i22i2−2i2−2i22i20000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ864-4-4-4-444444-4-4-444-40000000000000000-440000000000000000000000000000000000000000000000000000

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