Finite Group Databasebeta

← Group #13178

Character table — Group #13178

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order12222222444444448888888844888816161616161616161616161616161616444444444444
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91-1111-1-1-1-1-111-1-11111-1-1-1-1111-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−i
χ101-1111-1-1-1-1-111-1-11111-1-1-1-1111-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii
χ111-1111-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−ii
χ121-1111-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−i
χ131-1111-1-1-1-1-1-1-1111111-1-1-1-111-11-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ141-1111-1-1-1-1-1-1-1111111-1-1-1-111-11-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ151-1111-1-1-1-1-1-1-1111111-1-1-1-111-11-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−i
χ161-1111-1-1-1-1-1-1-1111111-1-1-1-111-11-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1922222222-2-22222-2-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ2022222222-2-22222-2-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ2122222222-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−222000000000000
χ2222222222-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−2000000000000
χ23222-2-22-2-22-200002-22222-2-2-2-200000000000000000000002-22-200000000
χ24222-2-22-2-22-200002-22222-2-2-2-20000000000000000000000-22-2200000000
χ25222-2-22-2-22-200002-2-2-2-2-22222000000000000000000000000002i−2i2i−2i0000
χ26222-2-22-2-22-200002-2-2-2-2-2222200000000000000000000000000−2i2i−2i2i0000
χ2722-22-2-2-22002i−2i2i−2i002−22−22−22−200i2−i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ2822-22-2-2-22002i−2i2i−2i002−22−22−22−200i2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ2922-22-2-2-22002i−2i2i−2i00−22−22−22−2200−i2i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3022-22-2-2-22002i−2i2i−2i00−22−22−22−2200−i2i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3122-22-2-2-2200−2i2i−2i2i002−22−22−22−200−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ3222-22-2-2-2200−2i2i−2i2i002−22−22−22−200−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ3322-22-2-2-2200−2i2i−2i2i00−22−22−22−2200i2−i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3422-22-2-2-2200−2i2i−2i2i00−22−22−22−2200i2−i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ352-2222-2-2-22222-2-2-2-200000000-22000022−2−2−2−22222−2−2−2−222000000000000
χ362-2222-2-2-22222-2-2-2-200000000-220000−2−22222−2−2−2−22222−2−2000000000000
χ372-2222-2-2-222-2-222-2-2000000002-2000022−2−2−2−222−2−22222−2−2000000000000
χ382-2222-2-2-222-2-222-2-2000000002-20000−2−22222−2−222−2−2−2−222000000000000
χ392-2222-2-2-2-2-222-2-222-2-22222-2-22-2-2-2220000000000000000000000000000
χ402-2222-2-2-2-2-2-2-22222-2-22222-2-2-2222-2-20000000000000000000000000000
χ412-22-2-2-222-2200002-222-2-222-2-200000000000000000000002i−2i−2i2i00000000
χ422-22-2-2-222-2200002-222-2-222-2-20000000000000000000000−2i2i2i−2i00000000
χ432-22-2-2-222-2200002-2-2-222-2-222000000000000000000000000002-2-220000
χ442-22-2-2-222-2200002-2-2-222-2-22200000000000000000000000000-222-20000
χ452-2-22-222-2002i−2i−2i2i002−2−22−222−200i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ462-2-22-222-2002i−2i−2i2i002−2−22−222−200i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ472-2-22-222-2002i−2i−2i2i00−222−22−2−2200−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ482-2-22-222-2002i−2i−2i2i00−222−22−2−2200−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ492-2-22-222-200−2i2i2i−2i002−2−22−222−200−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ502-2-22-222-200−2i2i2i−2i002−2−22−222−200−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ512-2-22-222-200−2i2i2i−2i00−222−22−2−2200i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ522-2-22-222-200−2i2i2i−2i00−222−22−2−2200i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ53444-4-44-4-4-440000-44000000000000000000000000000000000000000000
χ5444-4-44-44-40000000022−2222−22−2222−22220000000000000000000000000000000000
χ5544-4-44-44-400000000−2222−222222−2222−220000000000000000000000000000000000
χ564-44-4-4-4444-40000-44000000000000000000000000000000000000000000
χ574-4-4-444-440000000022−22−222222−22−22220000000000000000000000000000000000
χ584-4-4-444-4400000000−222222−22−222222−220000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.