Finite Group Databasebeta

← Group #271959

Character table — Group #271959

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11112222222244444444444444444448888888888888888888888161616161616161616323232
order12222244444422224444444444488884444448888888888888888444444888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1-1
χ4111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ511111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-11-1
χ611111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1111-11
χ711111111111111-1-111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11-1-11-11
χ811111111111111-1-111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-111-11-1
χ9111111111111-1-1111-1-1-1-1111-1-1111111-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
χ10111111111111-1-1111-1-1-1-1111-1-1111111-1-11-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1
χ11111111111111-1-1111-1-1-1-1111-1-11-1-1-1-11-1-11-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111111-1
χ12111111111111-1-1111-1-1-1-1111-1-11-1-1-1-11-1-11-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-11
χ13111111111111-1-1-1-11-1-1-1-1-1-11-1-111111-111-111-1-1-1-111111111-1-1-1-1-1-111111-1-11-1-1
χ14111111111111-1-1-1-11-1-1-1-1-1-11-1-111111-111-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-111-111
χ15111111111111-1-1-1-11-1-1-1-1-1-11-1-11-1-1-1-1-111-1111111-1-1-1-111-1-11111-1-111-1-11-1-1-111
χ16111111111111-1-1-1-11-1-1-1-1-1-11-1-11-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1111111-1-111-1111-1-1
χ172222222-222-222222-2-2-22222-2-2-2-20000-222-2-2-20000000000000000000000000000
χ182222222-222-2222-2-2-2-2-222-2-2-2-2-2-200002-2-22220000000000000000000000000000
χ192222222-222-22-2-222-222-2-222-222-20000-2-2-2-2220000000000000000000000000000
χ202222222-222-22-2-2-2-2-222-2-2-2-2-222-200002222-2-20000000000000000000000000000
χ212222-2-2222-22-20022-20000-2-2-20022222200-20022-2-2000000-2-20000000000000000
χ222222-2-2222-22-20022-20000-2-2-2002-2-2-2-2200-200-2-222000000220000000000000000
χ232222-2-2222-22-200-2-2-2000022-20022222-200200-2-222000000-2-20000000000000000
χ242222-2-2222-22-200-2-2-2000022-2002-2-2-2-2-20020022-2-2000000220000000000000000
χ252222-2-22-22-2-2-2002220000-2-2200-20000-20020000002i2i−2i−2i00002i2i−2i−2i000000000000
χ262222-2-22-22-2-2-2002220000-2-2200-20000-2002000000−2i−2i2i2i0000−2i−2i2i2i000000000000
χ272222-2-22-22-2-2-200-2-22000022200-20000200-20000002i2i−2i−2i0000−2i−2i2i2i000000000000
χ282222-2-22-22-2-2-200-2-22000022200-20000200-2000000−2i−2i2i2i00002i2i−2i−2i000000000000
χ292222-2-2-22-22222200-222-2-2002-2-2-2000000000000000000220000002-20000-200000
χ302222-2-2-22-22222200-222-2-2002-2-2-2000000000000000000-2-2000000-220000200000
χ312222-2-2-22-2222-2-200-2-2-22200222-200000000000000000022000000-220000-200000
χ322222-2-2-22-2222-2-200-2-2-22200222-2000000000000000000-2-20000002-20000200000
χ332222-2-2-2-2-22-2222002-2-2-2-200-222200000000000000000000000000002-20002-2000
χ342222-2-2-2-2-22-2222002-2-2-2-200-22220000000000000000000000000000-22000-22000
χ352222-2-2-2-2-22-22-2-2002222200-2-2-2200000000000000000000000000002-2000-22000
χ362222-2-2-2-2-22-22-2-2002222200-2-2-220000000000000000000000000000-220002-2000
χ372-22-22-2-202-202002-202i−2i002-202i−2i0i2i2−i2−i200002i−2ii2−i2i2−i22−22−200i2−i22−22−2000000000000
χ382-22-22-2-202-202002-202i−2i002-202i−2i0−i2−i2i2i200002i−2i−i2i2−i2i2−22−2200−i2i2−22−22000000000000
χ392-22-22-2-202-202002-20−2i2i002-20−2i2i0i2i2−i2−i20000−2i2ii2−i2i2−i2−22−2200i2−i2−22−22000000000000
χ402-22-22-2-202-202002-20−2i2i002-20−2i2i0−i2−i2i2i20000−2i2i−i2i2−i2i22−22−200−i2i22−22−2000000000000
χ412-22-22-2-202-20200-2202i−2i00-2202i−2i0i2i2−i2−i20000−2i2i−i2i2−i2i2−22−2200i2−i22−22−2000000000000
χ422-22-22-2-202-20200-2202i−2i00-2202i−2i0−i2−i2i2i20000−2i2ii2−i2i2−i22−22−200−i2i2−22−22000000000000
χ432-22-22-2-202-20200-220−2i2i00-220−2i2i0i2i2−i2−i200002i−2i−i2i2−i2i22−22−200i2−i2−22−22000000000000
χ442-22-22-2-202-20200-220−2i2i00-220−2i2i0−i2−i2i2i200002i−2ii2−i2i2−i2−22−2200−i2i22−22−2000000000000
χ452-22-2-22-20220-22-22-20002-2-220000i2i2−i2−i202-2000i2−i2−i2i2i2−i2−i2i200−i2i2i2−i2−i2i2000000000000
χ462-22-2-22-20220-22-22-20002-2-220000−i2−i2i2i202-2000−i2i2i2−i2−i2i2i2−i200i2−i2−i2i2i2−i2000000000000
χ472-22-2-22-20220-22-2-220002-22-20000i2i2−i2−i20-22000−i2i2i2−i2−i2i2i2−i200−i2i2i2−i2−i2i2000000000000
χ482-22-2-22-20220-22-2-220002-22-20000−i2−i2i2i20-22000i2−i2−i2i2i2−i2−i2i200i2−i2−i2i2i2−i2000000000000
χ492-22-2-22-20220-2-222-2000-22-220000i2i2−i2−i20-22000i2−i2−i2i2−i2i2i2−i200−i2i2−i2i2i2−i2000000000000
χ502-22-2-22-20220-2-222-2000-22-220000−i2−i2i2i20-22000−i2i2i2−i2i2−i2−i2i200i2−i2i2−i2−i2i2000000000000
χ512-22-2-22-20220-2-22-22000-222-20000i2i2−i2−i202-2000−i2i2i2−i2i2−i2−i2i200−i2i2−i2i2i2−i2000000000000
χ522-22-2-22-20220-2-22-22000-222-20000−i2−i2i2i202-2000i2−i2−i2i2−i2i2i2−i200i2−i2i2−i2−i2i2000000000000
χ53444444-44-4-44-400004000000-400-400000000000000000000000000000000000000
χ54444444-4-4-4-4-4-40000-4000000400400000000000000000000000000000000000000
χ5544-4-4000400-4000000000000000022−2222−220000000000000022−2200000000002-2000000
χ5644-4-4000400-4000000000000000022−2222−2200000000000000−22220000000000-22000000
χ5744-4-4000400-40000000000000000−2222−22220000000000000022−220000000000-22000000
χ5844-4-4000400-40000000000000000−2222−222200000000000000−222200000000002-2000000
χ594-44-44-440-440-44-400000-4400000000000000000000000000000000000000000000
χ604-44-44-440-440-4-44000004-400000000000000000000000000000000000000000000
χ614-44-4-4440-4-404000004i−4i00000−4i4i000000000000000000000000000000000000000
χ624-44-4-4440-4-40400000−4i4i000004i−4i000000000000000000000000000000000000000
χ6388-8-8000-8008000000000000000000000000000000000000000000000000000000
χ648-8-88000000000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ658-8-8800000000000000000000000−4i4i4i−4i0000000000000000000000000000000000

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