Finite Group Databasebeta

← Group #12866

Character table — Group #12866

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11111111222222222222222244444444444444444444448888888816161616
order12222222222244448888888844888816161616161616161616161616161616444444444444
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
χ511111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911-1-11-1-1111-1-11-1-111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ1011-1-11-1-1111-1-11-1-111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ1111-1-11-1-1111-1-11-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ1211-1-11-1-1111-1-11-1-111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ1311-1-11-1-11-1-1111-1-111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ1411-1-11-1-11-1-1111-1-111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ1511-1-11-1-11-1-1111-1-111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ1611-1-11-1-11-1-1111-1-111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ19222222222222-2-2-2-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ2022222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
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
χ2322-2-22-2-2222-2-22-2-22-2-2-2-222222-2-2-2220000000000000000000000000000
χ2422-2-22-2-2222-2-2-222-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2522-2-22-2-2222-2-2-222-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2622-2-22-2-22-2-2222-2-22-2-2-2-22222-2222-2-20000000000000000000000000000
χ2722-2-22-2-22-2-222-222-2000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822-2-22-2-22-2-222-222-2000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ292-222-2-2-222-22-2000022−2−222−2−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ302-222-2-2-222-22-2000022−2−222−2−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ312-222-2-2-222-22-20000−2−222−2−22200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ322-222-2-2-222-22-20000−2−222−2−22200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ332-222-2-2-22-22-22000022−2−222−2−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ342-222-2-2-22-22-22000022−2−222−2−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ352-222-2-2-22-22-220000−2−222−2−222002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ362-222-2-2-22-22-220000−2−222−2−222002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ372-22-222-2-20000-22-222-22-22-22-2000000000000000000000000002i−2i2i−2i0000
χ382-22-222-2-20000-22-222-22-22-22-200000000000000000000000000−2i2i−2i2i0000
χ392-22-222-2-20000-22-22-22-22-22-2200000000000000000000002i−2i2i−2i00000000
χ402-22-222-2-20000-22-22-22-22-22-220000000000000000000000−2i2i−2i2i00000000
χ412-2-222-22-20000-2-2222-22-2-22-22000000000000000000000000002i−2i−2i2i0000
χ422-2-222-22-20000-2-2222-22-2-22-2200000000000000000000000000−2i2i2i−2i0000
χ432-2-222-22-20000-2-222-22-222-22-200000000000000000000002i−2i−2i2i00000000
χ442-2-222-22-20000-2-222-22-222-22-20000000000000000000000−2i2i2i−2i00000000
χ452-2-2-2-22222-2-22000022−2−2−2−222002−2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ462-2-2-2-22222-2-22000022−2−2−2−222002−2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ472-2-2-2-22222-2-220000−2−22222−2−200−222−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ482-2-2-2-22222-2-220000−2−22222−2−200−222−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ492-2-2-2-2222-222-2000022−2−2−2−22200−222−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ502-2-2-2-2222-222-2000022−2−2−2−22200−222−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ512-2-2-2-2222-222-20000−2−22222−2−2002−2−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ522-2-2-2-2222-222-20000−2−22222−2−2002−2−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ53444-4-4-44-40000000022−22−222222−22−22220000000000000000000000000000000000
χ54444-4-4-44-400000000−222222−22−222222−220000000000000000000000000000000000
χ5544-44-44-4-40000000022−22−2222−222222−220000000000000000000000000000000000
χ5644-44-44-4-400000000−222222−2222−22−22220000000000000000000000000000000000
χ574-44-444-4-400004-44-4000000000000000000000000000000000000000000
χ584-4-444-44-4000044-4-4000000000000000000000000000000000000000000

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