Finite Group Databasebeta

← Group #140276

Character table — Group #140276

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888448888888888888888888816161616161616161616161616161616444488884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−ii−i11-1-11-1i−i
χ101-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−ii−ii-1-111-11−ii
χ111-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111i−ii−i11-1-1-11−ii
χ121-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−ii−ii-1-1111-1i−i
χ131-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111i−ii−i-1-1111-1−ii
χ141-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−ii−ii11-1-1-11i−i
χ151-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1i−ii−i-1-111-11i−i
χ161-1-111-11-11-1-1-1-111111-1-111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii−ii11-1-11-1−ii
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222-2-222-2-2200000000-2-2000022-2-222-2-20000000022−2−222−2−222−2−222−2−2000000000000
χ20222222222-2-222-2-2200000000-2-2000022-2-222-2-200000000−2−222−2−222−2−222−2−222000000000000
χ21222222222-2-222-2-2200000000-2-20000-2-222-2-2220000000022−2−222−2−2−2−222−2−222000000000000
χ22222222222-2-222-2-2200000000-2-20000-2-222-2-22200000000−2−222−2−22222−2−222−2−2000000000000
χ2322222222-222-2-222-222222222-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ2422222222-222-2-222-222222222-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ2522222222-222-2-222-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-222-2-222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i−2i2i0000
χ272222-2-2-2-22002-200-22−22−22−22−2002−22−2002-2002-222−2−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ282222-2-2-2-22002-200-22−22−22−22−2002−22−2002-2002-222−2−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ292222-2-2-2-22002-200-22−22−22−22−2002−22−200-2200-22−2−222−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ302222-2-2-2-22002-200-22−22−22−22−2002−22−200-2200-22−2−222−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ312222-2-2-2-22002-200-2−22−22−22−2200−22−22002-2002-2−2−222−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ322222-2-2-2-22002-200-2−22−22−22−2200−22−22002-2002-2−2−222−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ332222-2-2-2-22002-200-2−22−22−22−2200−22−2200-2200-2222−2−222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ342222-2-2-2-22002-200-2−22−22−22−2200−22−2200-2200-2222−2−222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ352-2-222-22-2222-2-2-2-2200000000-2200002i2i−2i−2i−2i−2i2i2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ362-2-222-22-2222-2-2-2-2200000000-2200002i2i−2i−2i−2i−2i2i2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ372-2-222-22-2222-2-2-2-2200000000-220000−2i−2i2i2i2i2i−2i−2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ382-2-222-22-2222-2-2-2-2200000000-220000−2i−2i2i2i2i2i−2i−2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ392-2-222-22-22-2-2-2-2222-2-222-2-2222-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ402-2-222-22-22-2-2-2-2222-2-222-2-2222-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ412-2-222-22-2-2-2-22222-222-2-222-2-2-22-2-222000000000000000000000000000000002i−2i−2i2i00000000
χ422-2-222-22-2-2-2-22222-222-2-222-2-2-22-2-22200000000000000000000000000000000−2i2i2i−2i00000000
χ432-2-222-22-2-2-2-22222-2-2-222-2-222-2222-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ442-2-222-22-2-2-2-22222-2-2-222-2-222-2222-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ452-2-22-22-22200-2200-22−2−222−2−22002−2−22002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ462-2-22-22-22200-2200-22−2−222−2−22002−2−22002i−2i00−2i2ii2i2−i2−i2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ472-2-22-22-22200-2200-22−2−222−2−22002−2−2200−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ482-2-22-22-22200-2200-22−2−222−2−22002−2−2200−2i2i002i−2i−i2−i2i2i2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ492-2-22-22-22200-2200-2−222−2−222−200−222−2002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ502-2-22-22-22200-2200-2−222−2−222−200−222−2002i−2i00−2i2i−i2−i2i2i2i2i2−i2−i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ512-2-22-22-22200-2200-2−222−2−222−200−222−200−2i2i002i−2ii2i2−i2−i2−i2−i2i2i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ522-2-22-22-22200-2200-2−222−2−222−200−222−200−2i2i002i−2ii2i2−i2−i2−i2−i2i2i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-400-4400422−2222−2222−2222−2200−2222−222200000000000000000000000000000000000000000000
χ554444-4-4-4-4-400-44004−2222−2222−2222−22220022−2222−2200000000000000000000000000000000000000000000
χ5644-4-444-4-40000000022−22−2222−222222−2200000022−220022−22002-22-22-22-20000000000000000000000000000
χ5744-4-444-4-40000000022−22−2222−222222−22000000−222200−222200-22-22-22-220000000000000000000000000000
χ5844-4-444-4-400000000−222222−2222−22−222200000022−220022−2200-22-22-22-220000000000000000000000000000
χ5944-4-444-4-400000000−222222−2222−22−2222000000−222200−2222002-22-22-22-20000000000000000000000000000
χ6044-4-4-4-44404-4004-40000000000000000000000022−22−222222−22−22220000000000000000000000000000
χ6144-4-4-4-44404-4004-400000000000000000000000−222222−22−222222−220000000000000000000000000000
χ6244-4-4-4-4440-4400-44044-4-4-4-44400000000000000000000000000000000000000000000000000
χ6344-4-4-4-4440-4400-440-4-44444-4-400000000000000000000000000000000000000000000000000
χ644-44-44-4-440000000022−2222−22−2222−22220000002i2−2i200−2i22i2002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ654-44-44-4-440000000022−2222−22−2222−2222000000−2i22i2002i2−2i200−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ664-44-44-4-4400000000−2222−222222−2222−220000002i2−2i200−2i22i200−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ674-44-44-4-4400000000−2222−222222−2222−22000000−2i22i2002i2−2i2002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ684-44-4-444-404-400-4404444-4-4-4-400000000000000000000000000000000000000000000000000
χ694-44-4-444-404-400-440-4-4-4-4444400000000000000000000000000000000000000000000000000
χ704-44-4-444-40-44004-4000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ714-44-4-444-40-44004-400000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ724-4-444-44-4-44444-4-4-4000000004-4000000000000000000000000000000000000000000000000
χ734-4-44-44-44-4004-400422−22−222222−22−222200−222222−2200000000000000000000000000000000000000000000
χ744-4-44-44-44-4004-4004−222222−22−222222−220022−22−222200000000000000000000000000000000000000000000

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