Finite Group Databasebeta

← Group #93921

Character table — Group #93921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444488884444881616161616161616881616161632323232323232323232323232323232888888882488
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
χ511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111-1-111-1-1-1-1-1-1i−ii−i11ii−i−iii−i−ii−i11-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ61-1i−i
χ101111-1-111-1-1-1-1-1-1i−ii−i11ii−i−iii−i−ii−i11-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6-11−ii
χ111111-1-111-1-1-1-1-1-1i−ii−i11ii−i−iii−i−ii−i11-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6-11−ii
χ121111-1-111-1-1-1-1-1-1i−ii−i11ii−i−iii−i−ii−i11-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ61-1i−i
χ131111-1-111-1-1-1-1-1-1−ii−ii11−i−iii−i−iii−ii11-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ21-1−ii
χ141111-1-111-1-1-1-1-1-1−ii−ii11−i−iii−i−iii−ii11-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2-11i−i
χ151111-1-111-1-1-1-1-1-1−ii−ii11−i−iii−i−iii−ii11-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2-11i−i
χ161111-1-111-1-1-1-1-1-1−ii−ii11−i−iii−i−iii−ii11-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ21-1−ii
χ1722222222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-22222222222-2-2-2-2-2-20000000000000000000000000000
χ192222222222-2-2-2-22222-2-200000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-22222-2-200000000-2-20000−2−222−2−222−2−222−2−222000000000000
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
χ232222-2-222-2-222222i−2i2i−2i-2-200000000−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000
χ242222-2-222-2-222222i−2i2i−2i-2-200000000−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000
χ252222-2-222-2-22222−2i2i−2i2i-2-2000000002i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000000000
χ262222-2-222-2-22222−2i2i−2i2i-2-2000000002i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000
χ272222-2-222-2-2-2-2-2-22i−2i2i−2i22−2i−2i2i2i−2i−2i2i2i2i−2i-2-2220000000000000000000000000000
χ282222-2-222-2-2-2-2-2-2−2i2i−2i2i222i2i−2i−2i2i2i−2i−2i−2i2i-2-2220000000000000000000000000000
χ292-2-222-22-22-200002i−2i−2i2i00i2−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
χ302-2-222-22-22-200002i−2i−2i2i00i2−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
χ312-2-222-22-22-200002i−2i−2i2i00−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
χ322-2-222-22-22-200002i−2i−2i2i00−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
χ332-2-222-22-22-20000−2i2i2i−2i00i2−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
χ342-2-222-22-22-20000−2i2i2i−2i00i2−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
χ352-2-222-22-22-20000−2i2i2i−2i00−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
χ362-2-222-22-22-20000−2i2i2i−2i00−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
χ372-2-222-2-22-22-2-22200002-22222-2-2-2-20000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ382-2-222-2-22-22-2-22200002-22222-2-2-2-20000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ392-2-222-2-22-22-2-22200002-2-2-2-2-2222200000000000000000000002−22−2−22−220000
χ402-2-222-2-22-22-2-22200002-2-2-2-2-222220000000000000000000000−22−222−22−20000
χ412-2-22-222-2-22000022-2-2002−2−222−2−22002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ422-2-22-222-2-22000022-2-2002−2−222−2−22002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ432-2-22-222-2-22000022-2-200−222−2−222−200−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ442-2-22-222-2-22000022-2-200−222−2−222−200−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ452-2-22-222-2-220000-2-222002−2−222−2−2200−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ462-2-22-222-2-220000-2-222002−2−222−2−2200−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ472-2-22-222-2-220000-2-22200−222−2−222−2002−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ482-2-22-222-2-220000-2-22200−222−2−222−2002−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ492-2-22-22-222-222-2-200002-22i2i−2i−2i−2i−2i2i2i00000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000
χ502-2-22-22-222-222-2-200002-22i2i−2i−2i−2i−2i2i2i0000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000
χ512-2-22-22-222-222-2-200002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000
χ522-2-22-22-222-222-2-200002-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000
χ53444444-4-4-4-400000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ54444444-4-4-4-40000000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ554444-4-4-4-444000000000022−22−2222−222222−220000000000000000000000000000000000
χ564444-4-4-4-4440000000000−222222−2222−22−22220000000000000000000000000000000000
χ574-4-444-4-44-4444-4-40000-44000000000000000000000000000000000000000000
χ584-4-44-44-444-4-4-4440000-44000000000000000000000000000000000000000000
χ5988-8-80000004i2−4i24i2−4i2000000000000000000000000000000000000000000000000
χ6088-8-8000000−4i24i2−4i24i2000000000000000000000000000000000000000000000000
χ618-88-80000004i2−4i2−4i24i2000000000000000000000000000000000000000000000000
χ628-88-8000000−4i24i24i2−4i2000000000000000000000000000000000000000000000000

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