Finite Group Databasebeta

← Group #122607

Character table — Group #122607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444444442244448888888844888816161616161616161616161616161616888888884444
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
χ511111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ9111111-1-1-1-1-1-111111-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ10111111-1-1-1-1-1-111111-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ11111111-1-1-1-1-1-111111-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ12111111-1-1-1-1-1-111111-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ13111111-1-1-1-1-1-111-1-11-111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ14111111-1-1-1-1-1-111-1-11-111-1-1-1-11111-1111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ15111111-1-1-1-1-1-111-1-11-111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ16111111-1-1-1-1-1-111-1-11-111-1-1-1-11111-1111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222222-2-222-2-222222222-2-2-2-2-2-20000000000000000000000000000
χ192222222222-2-2-2-222-2-22200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-222-2-22200000000-2-20000−2−222−2−222−2−222−2−222000000000000
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
χ23222222-2-2-2-222-2-222-22-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ24222222-2-2-2-222-2-222-22-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ25222222-2-2-2-222-2-2-2-2-2222000000002-2000022−2−2−2−222−2−22222−2−2000000000000
χ26222222-2-2-2-222-2-2-2-2-2222000000002-20000−2−22222−2−222−2−2−2−222000000000000
χ27222222-2-2-2-2-2-222222-2-2-2-2-2-2-222222-2-2-2220000000000000000000000000000
χ28222222-2-2-2-2-2-222-2-22-2222222-2-2-2-2-22-2-2220000000000000000000000000000
χ292222-2-222-2-222-2-2002-2002i2i−2i−2i2i2i−2i−2i00000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ302222-2-222-2-222-2-2002-2002i2i−2i−2i2i2i−2i−2i0000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ312222-2-222-2-222-2-2002-200−2i−2i2i2i−2i−2i2i2i00000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ322222-2-222-2-222-2-2002-200−2i−2i2i2i−2i−2i2i2i0000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ332222-2-2-2-222-2-2-2-20022002i2i−2i−2i−2i−2i2i2i00000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ342222-2-2-2-222-2-2-2-20022002i2i−2i−2i−2i−2i2i2i0000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ352222-2-2-2-222-2-2-2-2002200−2i−2i2i2i2i2i−2i−2i00000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ362222-2-2-2-222-2-2-2-2002200−2i−2i2i2i2i2i−2i−2i0000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ372-22-22-22i−2i2i−2i00002-2002i−2i2−22−2i2−i2i2−i2002−2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ382-22-22-22i−2i2i−2i00002-2002i−2i2−22−2i2−i2i2−i2002−2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ392-22-22-22i−2i2i−2i00002-2002i−2i−22−22−i2i2−i2i200−22−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ402-22-22-22i−2i2i−2i00002-2002i−2i−22−22−i2i2−i2i200−22−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ412-22-22-22i−2i2i−2i0000-2200−2i2i2−22−2i2−i2i2−i200−22−i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ422-22-22-22i−2i2i−2i0000-2200−2i2i2−22−2i2−i2i2−i200−22−i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ432-22-22-22i−2i2i−2i0000-2200−2i2i−22−22−i2i2−i2i2002−2i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ442-22-22-22i−2i2i−2i0000-2200−2i2i−22−22−i2i2−i2i2002−2i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ452-22-22-2−2i2i−2i2i00002-200−2i2i2−22−2−i2i2−i2i2002−2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000000000
χ462-22-22-2−2i2i−2i2i00002-200−2i2i2−22−2−i2i2−i2i2002−2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000000000
χ472-22-22-2−2i2i−2i2i00002-200−2i2i−22−22i2−i2i2−i200−22i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000000000
χ482-22-22-2−2i2i−2i2i00002-200−2i2i−22−22i2−i2i2−i200−22i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000000000
χ492-22-22-2−2i2i−2i2i0000-22002i−2i2−22−2−i2i2−i2i200−22i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000000000
χ502-22-22-2−2i2i−2i2i0000-22002i−2i2−22−2−i2i2−i2i200−22i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000000000
χ512-22-22-2−2i2i−2i2i0000-22002i−2i−22−22i2−i2i2−i2002−2−i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000000000
χ522-22-22-2−2i2i−2i2i0000-22002i−2i−22−22i2−i2i2−i2002−2−i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000000000
χ534444-4-444-4-4-4-44400-4400000000000000000000000000000000000000000000
χ544444-4-4-4-444444400-4-400000000000000000000000000000000000000000000
χ554-44-4-444i−4i−4i4i00000000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000
χ564-44-4-444i−4i−4i4i0000000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000
χ574-44-4-44−4i4i4i−4i00000000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000
χ584-44-4-44−4i4i4i−4i0000000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000
χ5988-8-8000000008-8000000000000000000000000000000000000000000000000
χ6088-8-800000000-88000000000000000000000000000000000000000000000000
χ618-8-880000008i−8i00000000000000000000000000000000000000000000000000
χ628-8-88000000−8i8i00000000000000000000000000000000000000000000000000

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