Finite Group Databasebeta

← Group #13015

Character table — Group #13015

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
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
χ9111-1-1-1-11ii−i−i1-11-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1i−i1-1
χ10111-1-1-1-11ii−i−i1-11-111-1-111-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111−ii-11
χ11111-1-1-1-11ii−i−i1-11-111-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1−ii-11
χ12111-1-1-1-11ii−i−i1-11-111-1-111-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii−i−iii-1-111i−i1-1
χ13111-1-1-1-11−i−iii1-11-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111i−i-11
χ14111-1-1-1-11−i−iii1-11-111-1-111-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1−ii1-1
χ15111-1-1-1-11−i−iii1-11-111-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−iii−i−i-1-111−ii1-1
χ16111-1-1-1-11−i−iii1-11-111-1-111-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1i−i-11
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
χ23222-2-2-2-222i2i−2i−2i2-22-2-2-222-2-2222i−2i−2i−2i2i2i0000000000000000000000000000
χ24222-2-2-2-222i2i−2i−2i-22-2200000000−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ25222-2-2-2-222i2i−2i−2i-22-2200000000−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ26222-2-2-2-22−2i−2i2i2i2-22-2-2-222-2-222−2i2i2i2i−2i−2i0000000000000000000000000000
χ27222-2-2-2-22−2i−2i2i2i-22-22000000002i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ28222-2-2-2-22−2i−2i2i2i-22-22000000002i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ2922-222-2-2-22-22-200002−22−22−22−2002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3022-222-2-2-22-22-200002−22−22−22−2002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3122-222-2-2-22-22-20000−22−22−22−2200−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ3222-222-2-2-22-22-20000−22−22−22−2200−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3322-222-2-2-2-22-2200002−22−22−22−200−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ3422-222-2-2-2-22-2200002−22−22−22−200−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ3522-222-2-2-2-22-220000−22−22−22−22002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ3622-222-2-2-2-22-220000−22−22−22−22002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ3722-2-2-222-22i−2i−2i2i00002−2−222−2−2200i2−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
χ3822-2-2-222-22i−2i−2i2i00002−2−222−2−2200i2−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
χ3922-2-2-222-22i−2i−2i2i0000−222−2−222−200−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
χ4022-2-2-222-22i−2i−2i2i0000−222−2−222−200−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
χ4122-2-2-222-2−2i2i2i−2i00002−2−222−2−2200−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
χ4222-2-2-222-2−2i2i2i−2i00002−2−222−2−2200−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
χ4322-2-2-222-2−2i2i2i−2i0000−222−2−222−200i2−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
χ4422-2-2-222-2−2i2i2i−2i0000−222−2−222−200i2−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
χ452-2-22-22-220000-222-22222-2-2-2-200000000000000000000002i−2i2i−2i00000000
χ462-2-22-22-220000-222-22222-2-2-2-20000000000000000000000−2i2i−2i2i00000000
χ472-2-22-22-220000-222-2-2-2-2-22222000000000000000000000000002-22-20000
χ482-2-22-22-220000-222-2-2-2-2-2222200000000000000000000000000-22-220000
χ492-2-2-22-2220000-2-22222-2-2-2-22200000000000000000000002-2-2200000000
χ502-2-2-22-2220000-2-22222-2-2-2-2220000000000000000000000-222-200000000
χ512-2-2-22-2220000-2-222-2-22222-2-2000000000000000000000000002-2-220000
χ522-2-2-22-2220000-2-222-2-22222-2-200000000000000000000000000-222-20000
χ534-444-4-44-40000000022−2222−22−2222−22220000000000000000000000000000000000
χ544-444-4-44-400000000−2222−222222−2222−220000000000000000000000000000000000
χ554-44-444-4-40000000022−22−2222−222222−220000000000000000000000000000000000
χ564-44-444-4-400000000−222222−2222−22−22220000000000000000000000000000000000
χ574-4-44-44-4400004-4-44000000000000000000000000000000000000000000
χ584-4-4-44-444000044-4-4000000000000000000000000000000000000000000

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