Finite Group Databasebeta

← Group #125113

Character table — Group #125113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order122222444488884444444488888824888816161616161616161616161616161616888888884444
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
χ511111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ91111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ161111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222222222222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2222222-2-2-2-2-2-2-2-2220000000000000000000000000000
χ192222222222-2-2-2-222222222-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2220000000000000000000000000000
χ21222222-2-2-2-2000022-2-222-2-20000002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ22222222-2-2-2-2000022-2-222-2-20000002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ23222222-2-2-2-2000022-2-2-2-222000000-22000022−2−2−2−22222−2−2−2−222000000000000
χ24222222-2-2-2-2000022-2-2-2-222000000-220000−2−22222−2−2−2−22222−2−2000000000000
χ25222222-2-2-2-20000-2-22222-2-2000000-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ26222222-2-2-2-20000-2-22222-2-2000000-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ27222222-2-2-2-20000-2-222-2-2220000002-2000022−2−222−2−2−2−222−2−222000000000000
χ28222222-2-2-2-20000-2-222-2-2220000002-20000−2−222−2−22222−2−222−2−2000000000000
χ292-22-22-22-22-2000000002i−2i2i−2i002i2i−2i−2i002-20000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000
χ302-22-22-22-22-2000000002i−2i2i−2i002i2i−2i−2i002-2000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000
χ312-22-22-22-22-2000000002i−2i2i−2i00−2i−2i2i2i00-22002ζ3−2ζ32ζ3−2ζ3000000002ζ−2ζ2ζ−2ζ000000000000
χ322-22-22-22-22-2000000002i−2i2i−2i00−2i−2i2i2i00-2200−2ζ32ζ3−2ζ32ζ300000000−2ζ2ζ−2ζ2ζ000000000000
χ332-22-22-22-22-200000000−2i2i−2i2i002i2i−2i−2i00-22002ζ−2ζ2ζ−2ζ000000002ζ3−2ζ32ζ3−2ζ3000000000000
χ342-22-22-22-22-200000000−2i2i−2i2i002i2i−2i−2i00-2200−2ζ2ζ−2ζ2ζ00000000−2ζ32ζ3−2ζ32ζ3000000000000
χ352-22-22-22-22-200000000−2i2i−2i2i00−2i−2i2i2i002-20000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000
χ362-22-22-22-22-200000000−2i2i−2i2i00−2i−2i2i2i002-2000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000
χ372-22-22-2-22-222i2i−2i−2i00002i−2i−2i2i2i−2i000000002-21+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ382-22-22-2-22-222i2i−2i−2i00002i−2i−2i2i2i−2i000000002-2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ392-22-22-2-22-222i2i−2i−2i0000−2i2i2i−2i2i−2i00000000-221−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ402-22-22-2-22-222i2i−2i−2i0000−2i2i2i−2i2i−2i00000000-22−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ412-22-22-2-22-22−2i−2i2i2i00002i−2i−2i2i−2i2i00000000-221+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ422-22-22-2-22-22−2i−2i2i2i00002i−2i−2i2i−2i2i00000000-22−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ432-22-22-2-22-22−2i−2i2i2i0000−2i2i2i−2i−2i2i000000002-21−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ442-22-22-2-22-22−2i−2i2i2i0000−2i2i2i−2i−2i2i000000002-2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ452-22-2-222-2-222i2i−2i−2i2i−2i2i−2i0000−2i2i2-22-20000000000000000000000i2−i22−22−2i2−i20000
χ462-22-2-222-2-222i2i−2i−2i2i−2i2i−2i0000−2i2i2-22-20000000000000000000000−i2i2−22−22−i2i20000
χ472-22-2-222-2-222i2i−2i−2i−2i2i−2i2i0000−2i2i-22-2200000000000000000000002−2−i2i2i2−i2−220000
χ482-22-2-222-2-222i2i−2i−2i−2i2i−2i2i0000−2i2i-22-220000000000000000000000−22i2−i2−i2i22−20000
χ492-22-2-222-2-22−2i−2i2i2i2i−2i2i−2i00002i−2i-22-2200000000000000000000002−2i2−i2−i2i2−220000
χ502-22-2-222-2-22−2i−2i2i2i2i−2i2i−2i00002i−2i-22-220000000000000000000000−22−i2i2i2−i22−20000
χ512-22-2-222-2-22−2i−2i2i2i−2i2i−2i2i00002i−2i2-22-20000000000000000000000i2−i2−22−22i2−i20000
χ522-22-2-222-2-22−2i−2i2i2i−2i2i−2i2i00002i−2i2-22-20000000000000000000000−i2i22−22−2−i2i20000
χ534444-4-444-4-4000000000000004i−4i−4i4i0000000000000000000000000000000000
χ544444-4-444-4-400000000000000−4i4i4i−4i0000000000000000000000000000000000
χ554444-4-4-4-444444400000000-4-400000000000000000000000000000000000000
χ564444-4-4-4-444-4-4-4-4000000004400000000000000000000000000000000000000
χ574-44-4-44-444-400004i−4i−4i4i00000000000000000000000000000000000000000000
χ584-44-4-44-444-40000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5988-8-800000042−4242−42000000000000000000000000000000000000000000000000
χ6088-8-8000000−4242−4242000000000000000000000000000000000000000000000000
χ618-8-880000004i2−4i2−4i24i2000000000000000000000000000000000000000000000000
χ628-8-88000000−4i24i24i2−4i2000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.