Finite Group Databasebeta

← Group #122604

Character table — Group #122604

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222222244444444448888888844888816161616161616161616161616161616888888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ911111-1-1-1-111-1-111-111-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111-1-1-1-111-1-111-111-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111-1-1-1-111-1-111-111-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111-1-1-1-111-1-111-111-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111-1-1-1-111-1-111-1-1-111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111-1-1-1-111-1-111-1-1-111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111-1-1-1-111-1-111-1-1-111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111-1-1-1-111-1-111-1-1-111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-222222222-2-2-2-2-2-20000000000000000000000000000
χ192222222222-2-2-2-2-2-2222200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-2-2-2222200000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ222222222222-2-2-2-2-2-2-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2322222-2-2-2-222-2-222-222-2-2-2-2-2-222222-2-2-2220000000000000000000000000000
χ2422222-2-2-2-222-2-222-2-2-2222222-2-2-2-2-22-2-2220000000000000000000000000000
χ2522222-2-2-2-22-222-2-2222-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2622222-2-2-2-22-222-2-2222-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2722222-2-2-2-22-222-2-22-2-222000000002-2000022−2−2−2−222−2−22222−2−2000000000000
χ2822222-2-2-2-22-222-2-22-2-222000000002-20000−2−22222−2−222−2−2−2−222000000000000
χ292222-222-2-2-2-222-22-200002i2i−2i−2i2i2i−2i−2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ302222-222-2-2-2-222-22-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ312222-222-2-2-2-222-22-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ322222-222-2-2-2-222-22-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ332222-2-2-222-2-2-2-2-22200002i2i−2i−2i−2i−2i2i2i00000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ342222-2-2-222-2-2-2-2-22200002i2i−2i−2i−2i−2i2i2i0000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ352222-2-2-222-2-2-2-2-2220000−2i−2i2i2i2i2i−2i−2i00000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ362222-2-2-222-2-2-2-2-2220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ372-2-2222-22-2-20000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2002−22−2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ382-2-2222-22-2-20000002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2002−22−2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ392-2-2222-22-2-20000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200−22−22ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ402-2-2222-22-2-20000002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200−22−22−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ412-2-2222-22-2-2000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200−22−22ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ422-2-2222-22-2-2000000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200−22−22−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ432-2-2222-22-2-2000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2002−22−2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ442-2-2222-22-2-2000000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2002−22−2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ452-2-222-22-22-20000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2002−2−22ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ462-2-222-22-22-20000002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2002−2−22−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ472-2-222-22-22-20000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i200−222−2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ482-2-222-22-22-20000002i−2i−2i2i−i2i2−i2i2i2−i2i2−i200−222−2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ492-2-222-22-22-2000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i200−222−2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ502-2-222-22-22-2000000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i200−222−2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ512-2-222-22-22-2000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2002−2−22ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ522-2-222-22-22-2000000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2002−2−22−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ534444-444-4-4-44-4-44-440000000000000000000000000000000000000000000000
χ544444-4-4-444-44444-4-40000000000000000000000000000000000000000000000
χ554-4-44-44-4-444000000000022−22−222222−22−22220000000000000000000000000000000000
χ564-4-44-44-4-4440000000000−222222−22−222222−220000000000000000000000000000000000
χ574-4-44-4-444-44000000000022−22−2222−222222−220000000000000000000000000000000000
χ584-4-44-4-444-440000000000−222222−2222−22−22220000000000000000000000000000000000
χ5988-8-800000008i−8i0000000000000000000000000000000000000000000000000
χ6088-8-80000000−8i8i0000000000000000000000000000000000000000000000000
χ618-88-8000000800-8000000000000000000000000000000000000000000000000
χ628-88-8000000-8008000000000000000000000000000000000000000000000000

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