Finite Group Databasebeta

← Group #13616

Character table — Group #13616

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order12222244448888161616161616161688161616163232323232323232323232323232323222444444
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111-1-11-1-11111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111-1-11-1-11111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91-11-11-1-11-11-1-1111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101-11-11-1-11-11-1-1111111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111-11-11-1-11-11-1-1111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121-11-11-1-11-11-1-1111111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131-11-1-11-1-111-1-1111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11i−i−ii
χ141-11-1-11-1-111-1-1111111-1-1-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1−iii−i
χ151-11-1-11-1-111-1-1111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11−iii−i
χ161-11-1-11-1-111-1-1111111-1-1-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1i−i−ii
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ182222222222-2-2-2-200000000-2-2000022−2−222−2−222−2−222−2−200000000
χ192222222222-2-2-2-200000000-2-20000−2−222−2−222−2−222−2−22200000000
χ20222222-2-2-2-2000022−2−222−2−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ21222222-2-2-2-2000022−2−222−2−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ22222222-2-2-2-20000−2−222−2−22200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ23222222-2-2-2-20000−2−222−2−22200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ242222-2-22-2-222222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ252222-2-22-2-22-2-2-2-20000000022000022−2−222−2−2−2−222−2−22200000000
χ262222-2-22-2-22-2-2-2-200000000220000−2−222−2−22222−2−222−2−200000000
χ272222-2-2-222-2000022−2−222−2−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500000000
χ282222-2-2-222-2000022−2−222−2−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500000000
χ292222-2-2-222-20000−2−222−2−222002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700000000
χ302222-2-2-222-20000−2−222−2−222002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700000000
χ312-22-22-22-22-2000022−2−2−2−222002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ322-22-22-22-22-2000022−2−2−2−222002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ332-22-22-22-22-20000−2−22222−2−200−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ342-22-22-22-22-20000−2−22222−2−200−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ352-22-22-2-22-2222-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ362-22-22-2-22-2222-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ372-22-22-2-22-22-2-222-2-2-2-222222-2-2-222000000000000000000000000
χ382-22-2-2222-2-2000022−2−2−2−22200−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ392-22-2-2222-2-2000022−2−2−2−22200−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ402-22-2-2222-2-20000−2−22222−2−2002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ412-22-2-2222-2-20000−2−22222−2−2002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ422-22-2-22-2-22222-2-2000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ432-22-2-22-2-22222-2-2000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ442-22-2-22-2-222-2-222-2-2-2-22222-2222-2-2000000000000000000000000
χ4544-4-400000022−2222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000
χ4644-4-400000022−2222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ4744-4-4000000−2222−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ4844-4-4000000−2222−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ494-4-4400000022−22−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000
χ504-4-4400000022−22−2222−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000
χ514-4-44000000−222222−222ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000
χ524-4-44000000−222222−22−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000

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