Finite Group Databasebeta

← Group #139010

Character table — Group #139010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order122222444444888844488888888888888888888161616161616161616161616161616164444884488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111
χ711111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ9111111-111-1-1-1-1-1-1-11-1-111-1-1ii−i−i11i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1i−i1-1i−i
χ10111111-111-1-1-1-1-1-1-11-1-111-1-1ii−i−i11i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1i−i-11−ii
χ11111111-111-1-1-1-1-1-1-11-1-111-1-1ii−i−i11i−i−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−ii-11−ii
χ12111111-111-1-1-1-1-1-1-11-1-111-1-1ii−i−i11i−i−i−iiiii−i−i−i−i−i−iiiii-1-1-1-11111-1-111−ii1-1i−i
χ13111111-111-1-1-1-1-1-1-11-1-111-1-1−i−iii11−iiii−i−i−i−iiiiiii−i−i−i−i-1-1-1-11111-1-111i−i1-1−ii
χ14111111-111-1-1-1-1-1-1-11-1-111-1-1−i−iii11−iiii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-1-111i−i-11i−i
χ15111111-111-1-1-1-1-1-1-11-1-111-1-1−i−iii11−ii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1−ii-11i−i
χ16111111-111-1-1-1-1-1-1-11-1-111-1-1−i−iii11−ii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1−ii1-1−ii
χ17222222222222-2-2-2-2222-2-2-2-22222-2-2220000-2-2-2-200000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ192222222-2-22220000-2-2-20000222200-2-20000000022−2−222−2−222−2−222−2−20000000000
χ202222222-2-22220000-2-2-20000222200-2-200000000−2−222−2−222−2−222−2−2220000000000
χ212222222-2-22220000-2-2-20000-2-2-2-200220000000022−2−222−2−2−2−222−2−2220000000000
χ222222222-2-22220000-2-2-20000-2-2-2-2002200000000−2−222−2−22222−2−222−2−20000000000
χ23222222-222-2-2-222222-2-2-2-2222i2i−2i−2i-2-22i−2i0000−2i−2i2i2i00000000000000000000000000
χ24222222-222-2-2-222222-2-2-2-222−2i−2i2i2i-2-2−2i2i00002i2i−2i−2i00000000000000000000000000
χ25222222-2-2-2-2-2-20000-22200002i2i−2i−2i00−2i2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000
χ26222222-2-2-2-2-2-20000-22200002i2i−2i−2i00−2i2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000
χ27222222-2-2-2-2-2-20000-2220000−2i−2i2i2i002i−2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000
χ28222222-2-2-2-2-2-20000-2220000−2i−2i2i2i002i−2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000
χ292222-2-2222-22-22222-22-2-2-2-2-2000022000000000000000000000000002-22-2000000
χ302222-2-2222-22-22222-22-2-2-2-2-200002200000000000000000000000000-22-22000000
χ312222-2-2222-22-2-2-2-2-2-22-222220000-2-2002i2i−2i−2i000000000000000000000000−2i2i0000
χ322222-2-2222-22-2-2-2-2-2-22-222220000-2-200−2i−2i2i2i0000000000000000000000002i−2i0000
χ332222-2-2-2222-222222-2-2222-2-20000-2-2002222000000000000000000000000-2-20000
χ342222-2-2-2222-222222-2-2222-2-20000-2-200-2-2-2-2000000000000000000000000220000
χ352222-2-2-2222-22-2-2-2-2-2-22-2-222000022000000000000000000000000002-2-22000000
χ362222-2-2-2222-22-2-2-2-2-2-22-2-22200002200000000000000000000000000-222-2000000
χ372-2-222-2200-2-222−22−20002−22−22i−2i2i−2i2−2000000i2−i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ382-2-222-2200-2-222−22−20002−22−22i−2i2i−2i2−2000000i2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ392-2-222-2200-2-222−22−20002−22−2−2i2i−2i2i2−2000000−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ402-2-222-2200-2-222−22−20002−22−2−2i2i−2i2i2−2000000−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ412-2-222-2200-2-22−22−22000−22−222i−2i2i−2i−22000000−i2i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ422-2-222-2200-2-22−22−22000−22−222i−2i2i−2i−22000000−i2i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ432-2-222-2200-2-22−22−22000−22−22−2i2i−2i2i−22000000i2−i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ442-2-222-2200-2-22−22−22000−22−22−2i2i−2i2i−22000000i2−i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ452-2-222-2-20022-22−22−2000−222−22-2-22−22000000−222−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ462-2-222-2-20022-22−22−2000−222−22-2-22−22000000−222−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ472-2-222-2-20022-22−22−2000−222−2-222-2−220000002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000
χ482-2-222-2-20022-22−22−2000−222−2-222-2−220000002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000
χ492-2-222-2-20022-2−22−220002−2−222-2-222−20000002−2−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ502-2-222-2-20022-2−22−220002−2−222-2-222−20000002−2−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ512-2-222-2-20022-2−22−220002−2−22-222-22−2000000−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000
χ522-2-222-2-20022-2−22−220002−2−22-222-22−2000000−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000
χ534444-4-44-4-4-44-400004-440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-44-44000044-40000000000000000000000000000000000000000000000
χ5544-4-40004-400044-4-400000000000000022−2222−22000000000000000000000000000000
χ5644-4-40004-400044-4-4000000000000000−2222−2222000000000000000000000000000000
χ5744-4-40004-4000-4-4440000000000000002i2−2i2−2i22i2000000000000000000000000000000
χ5844-4-40004-4000-4-444000000000000000−2i22i22i2−2i2000000000000000000000000000000
χ594-4-44-444004-4-422−2222−22000−2222−2222000022−22000000000000000000000000000000000000
χ604-4-44-444004-4-4−2222−222200022−2222−220000−2222000000000000000000000000000000000000
χ614-4-44-44-400-44422−2222−2200022−22−22220000−2222000000000000000000000000000000000000
χ624-4-44-44-400-444−2222−2222000−222222−22000022−22000000000000000000000000000000000000
χ6388-8-8000-8800000000000000000000000000000000000000000000000000000000
χ648-88-80000000042−42−42420000000000000000000000000000000000000000000000000
χ658-88-800000000−424242−420000000000000000000000000000000000000000000000000

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