Finite Group Databasebeta

← Group #13494

Character table — Group #13494

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222222224444444444444444444444441616161616161616
order12222222444488888888224488881616161616161616161616161616161644444444
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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ9222222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ10222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ1122222222-2-2-2-20000000022-2-200002222−2−2−2−22222−2−2−2−200000000
χ1222222222-2-2-2-20000000022-2-20000−2−2−2−22222−2−2−2−2222200000000
χ1322222222-2-2-2-200000000-2-22200002222−2−2−2−2−2−2−2−2222200000000
χ1422222222-2-2-2-200000000-2-2220000−2−2−2−222222222−2−2−2−200000000
χ1522-222-2-2-22-2-2222-2-222-2-20000000000000000000000000000002i−2i
χ1622-222-2-2-22-2-2222-2-222-2-2000000000000000000000000000000−2i2i
χ1722-222-2-2-22-2-22-2-222-2-22200000000000000000000000000002i−2i00
χ1822-222-2-2-22-2-22-2-222-2-2220000000000000000000000000000−2i2i00
χ1922-2-2-222-200002−22−22−22−2002i−2ii2i2−i2−i2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500000000
χ2022-2-2-222-200002−22−22−22−2002i−2ii2i2−i2−i2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500000000
χ2122-2-2-222-200002−22−22−22−200−2i2i−i2−i2i2i2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500000000
χ2222-2-2-222-200002−22−22−22−200−2i2i−i2−i2i2i2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500000000
χ2322-2-2-222-20000−22−22−22−22002i−2i−i2−i2i2i2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700000000
χ2422-2-2-222-20000−22−22−22−22002i−2i−i2−i2i2i2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700000000
χ2522-2-2-222-20000−22−22−22−2200−2i2ii2i2−i2−i2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700000000
χ2622-2-2-222-20000−22−22−22−2200−2i2ii2i2−i2−i2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700000000
χ272-222-22-2-2-22-2222-2-2-2-2220000000000000000000000002i−2i000000
χ282-222-22-2-2-22-2222-2-2-2-222000000000000000000000000−2i2i000000
χ292-222-22-2-2-22-22-2-22222-2-2000000000000000000000000002i−2i0000
χ302-222-22-2-2-22-22-2-22222-2-200000000000000000000000000−2i2i0000
χ312-22-22-22-200002−22−2−22−222-2002−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ322-22-22-22-200002−22−2−22−222-2002−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ332-22-22-22-200002−22−2−22−22-2200−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ700000000
χ342-22-22-22-200002−22−2−22−22-2200−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ700000000
χ352-22-22-22-20000−22−222−22−22-200−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ362-22-22-22-20000−22−222−22−22-200−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ372-22-22-22-20000−22−222−22−2-22002−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ500000000
χ382-22-22-22-20000−22−222−22−2-22002−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ500000000
χ392-2-22-2-22222-2-20000000000002i−2i−2i2i2−2−222−2−22−i2i2i2−i2i2−i2−i2i200000000
χ402-2-22-2-22222-2-20000000000002i−2i−2i2i−222−2−222−2i2−i2−i2i2−i2i2i2−i200000000
χ412-2-22-2-22222-2-2000000000000−2i2i2i−2i2−2−222−2−22i2−i2−i2i2−i2i2i2−i200000000
χ422-2-22-2-22222-2-2000000000000−2i2i2i−2i−222−2−222−2−i2i2i2−i2i2−i2−i2i200000000
χ432-2-22-2-222-2-2222222-2-2-2-200000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ442-2-22-2-222-2-2222222-2-2-2-20000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ452-2-22-2-222-2-222-2-2-2-22222000000002-2-22-222-20000000000000000
χ462-2-22-2-222-2-222-2-2-2-2222200000000-222-22-2-220000000000000000
χ47444-4-4-4-44000022−22−222222−22−222200000000000000000000000000000000
χ48444-4-4-4-440000−222222−22−222222−2200000000000000000000000000000000
χ4944-444-4-4-4-444-40000000000000000000000000000000000000000
χ504-444-44-4-44-44-40000000000000000000000000000000000000000
χ514-4-4-444-44000022−22−2222−222222−2200000000000000000000000000000000
χ524-4-4-444-440000−222222−2222−22−222200000000000000000000000000000000

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