Finite Group Databasebeta

← Group #140311

Character table — Group #140311

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444448888888888888888888888161616161616161632323232
order1222444444444424888888888888444488888888888888888816161616161616164488
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
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111-1-111-1-1-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ10111111-1-111-1-1-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-11−ii
χ11111111-1-111-1-1-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-1-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ12111111-1-111-1-1-1-1-11iiii−i−i−i−i11-1-1ii−i−i1-1-1-1-1-11111−i−i−i−iiiii-1-111−i−iii1-1i−i
χ13111111-1-111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ14111111-1-111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i
χ15111111-1-111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−iii1-1-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-11i−i
χ16111111-1-111-1-1-1-1-11−i−i−i−iiiii11-1-1−i−iii1-1-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000
χ1922222222-2-2-2-2-2-22-20000000022-2-20000-22000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2022222222-2-2-2-2-2-22-20000000022-2-20000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2122222222-2-2-2-2-2-22-200000000-2-22200002-22i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2222222222-2-2-2-2-2-22-200000000-2-22200002-2−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ23222222-2-222-2-2-2-2-222i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i-220000000000000000000000000000
χ24222222-2-222-2-2-2-2-22−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i-220000000000000000000000000000
χ25222222-2-2-2-22222-2-20000000022220000-2-20000000022-2-2-2-222000000000000
χ26222222-2-2-2-22222-2-20000000022220000-2-200000000-2-22222-2-2000000000000
χ27222222-2-2-2-22222-2-200000000-2-2-2-20000222i2i−2i−2i−2i−2i2i2i00000000000000000000
χ28222222-2-2-2-22222-2-200000000-2-2-2-2000022−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292222-2-222-2-222-2-2-2222-2-222-2-200000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ302222-2-222-2-222-2-2-2222-2-222-2-200000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ312222-2-222-2-222-2-2-22-2-222-2-22200000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ322222-2-222-2-222-2-2-22-2-222-2-22200000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ332222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i00000000000000000000000000i2−i2−i2i2−222−20000
χ342222-2-2-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i00000000000000000000000000−i2i2i2−i22−2−220000
χ352222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000i2−i2−i2i22−2−220000
χ362222-2-2-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−i2i2i2−i2−222−20000
χ372-22-22-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i1+i−1−i1−i−1+i00i2−i2i2−i22−22−2002ζ3−2ζ32ζ−2ζ00000000000000
χ382-22-22-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i1+i−1−i1−i−1+i00−i2i2−i2i2−22−2200−2ζ32ζ3−2ζ2ζ00000000000000
χ392-22-22-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i−1−i1+i−1+i1−i002−2−22i2−i2−i2i22ζ−2ζ00002ζ3−2ζ3000000000000
χ402-22-22-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i−1−i1+i−1+i1−i00−222−2−i2i2i2−i2−2ζ2ζ0000−2ζ32ζ3000000000000
χ412-22-22-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i−1−i1+i−1+i1−i00i2−i2i2−i22−22−200−2ζ32ζ3−2ζ2ζ00000000000000
χ422-22-22-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i−1−i1+i−1+i1−i00−i2i2−i2i2−22−22002ζ3−2ζ32ζ−2ζ00000000000000
χ432-22-22-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i1+i−1−i1−i−1+i002−2−22i2−i2−i2i2−2ζ2ζ0000−2ζ32ζ3000000000000
χ442-22-22-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i1+i−1−i1−i−1+i00−222−2−i2i2i2−i22ζ−2ζ00002ζ3−2ζ3000000000000
χ452-22-22-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i1−i−1+i1+i−1−i00i2−i2i2−i2−22−22002ζ−2ζ2ζ3−2ζ300000000000000
χ462-22-22-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i1−i−1+i1+i−1−i00−i2i2−i2i22−22−200−2ζ2ζ−2ζ32ζ300000000000000
χ472-22-22-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i−1+i1−i−1−i1+i002−2−22−i2i2i2−i2−2ζ32ζ30000−2ζ2ζ000000000000
χ482-22-22-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i−1+i1−i−1−i1+i00−222−2i2−i2−i2i22ζ3−2ζ300002ζ−2ζ000000000000
χ492-22-22-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i−1+i1−i−1−i1+i00i2−i2i2−i2−22−2200−2ζ2ζ−2ζ32ζ300000000000000
χ502-22-22-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i−1+i1−i−1−i1+i00−i2i2−i2i22−22−2002ζ−2ζ2ζ3−2ζ300000000000000
χ512-22-22-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i1−i−1+i1+i−1−i002−2−22−i2i2i2−i22ζ3−2ζ300002ζ−2ζ000000000000
χ522-22-22-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i1−i−1+i1+i−1−i00−222−2i2−i2−i2i2−2ζ32ζ30000−2ζ2ζ000000000000
χ534444-4-44444-4-444-4-40000000000000000000000000000000000000000000000
χ544444-4-4-4-44444-4-44-40000000000000000000000000000000000000000000000
χ554-44-4-4400004i−4i−4i4i002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ564-44-4-4400004i−4i−4i4i00−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ574-44-4-440000−4i4i4i−4i002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ584-44-4-440000−4i4i4i−4i00−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ5988-8-800008-80000000000000000000000000000000000000000000000000000
χ6088-8-80000-880000000000000000000000000000000000000000000000000000
χ618-8-88008i−8i000000000000000000000000000000000000000000000000000000
χ628-8-8800−8i8i000000000000000000000000000000000000000000000000000000

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