Finite Group Databasebeta

← Group #137188

Character table — Group #137188

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order122222224444224488888888444416161616161616161616161616161616444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1
χ91-111-1-1-111-1-111-1-111111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−ii−ii−i11-1-11-111-1-1
χ101-111-1-1-111-1-111-1-111111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−ii−ii-1-1111-1-1-111
χ111-111-1-1-111-1-111-1-111111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−ii−ii−i-1-1111-1-1-111
χ121-111-1-1-111-1-111-1-111111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−ii−ii11-1-11-111-1-1
χ131-111-1-1-111-1-111-1-111111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii11-1-1-11-1-111
χ141-111-1-1-111-1-111-1-111111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i-1-111-1111-1-1
χ151-111-1-1-111-1-111-1-111111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii-1-111-1111-1-1
χ161-111-1-1-111-1-111-1-111111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i11-1-1-11-1-111
χ172222222222222222-2-2-2-2-2-2-2-222220000000000000000000000000000-2-20000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000220000
χ19222222222222-2-2-2-222-2-222-2-2000000000000000000002200-2-2000000000000
χ20222222222222-2-2-2-222-2-222-2-200000000000000000000-2-20022000000000000
χ21222222222222-2-2-2-2-2-222-2-22200000000000000000000002200-2-20000000000
χ22222222222222-2-2-2-2-2-222-2-2220000000000000000000000-2-200220000000000
χ2322222222-2-2-2-2-2-222000000002-22-222−2−222−2−222−2−222−2−2000000000000000000
χ2422222222-2-2-2-2-2-222000000002-22-2−2−222−2−222−2−222−2−222000000000000000000
χ2522222222-2-2-2-2-2-22200000000-22-2222−2−222−2−2−2−222−2−222000000000000000000
χ2622222222-2-2-2-2-2-22200000000-22-22−2−222−2−22222−2−222−2−2000000000000000000
χ272-222-2-2-222-2-222-2-22-2-2-2-2222222-2-20000000000000000000000000000-220000
χ282-222-2-2-222-2-222-2-22-2-2-2-22222-2-22200000000000000000000000000002-20000
χ292-222-2-2-222-2-22-222-222-2-2-2-222000000000000000000002i−2i00−2i2i000000000000
χ302-222-2-2-222-2-22-222-222-2-2-2-22200000000000000000000−2i2i002i−2i000000000000
χ312-222-2-2-222-2-22-222-2-2-22222-2-200000000000000000000002i−2i00−2i2i0000000000
χ322-222-2-2-222-2-22-222-2-2-22222-2-20000000000000000000000−2i2i002i−2i0000000000
χ332-222-2-2-22-222-2-22-22000000002-2-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000
χ342-222-2-2-22-222-2-22-22000000002-2-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000
χ352-222-2-2-22-222-2-22-2200000000-222-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000
χ362-222-2-2-22-222-2-22-2200000000-222-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000
χ3744444444-4-4-4-444-4-40000000000000000000000000000000000000000000000
χ38444-44-4-4-4000000000022−220022−220000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000000000000000
χ39444-44-4-4-4000000000022−220022−220000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000000000000000
χ40444-44-4-4-40000000000−222200−22220000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000000000000000
χ41444-44-4-4-40000000000−222200−22220000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000000000000000
χ4244-44-44-4-40000000022−220022−2200000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000000
χ4344-44-44-4-40000000022−220022−2200000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000000
χ4444-44-44-4-400000000−222200−222200000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000000
χ4544-44-44-4-400000000−222200−222200000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000000
χ4644-4-4-4-44444-4-400000000000000000000000000000000000000000000002i−2i2i−2i
χ4744-4-4-4-44444-4-40000000000000000000000000000000000000000000000−2i2i−2i2i
χ4844-4-4-4-444-4-44400000000000000000000000000000000000000002-22-2000000
χ4944-4-4-4-444-4-4440000000000000000000000000000000000000000-22-22000000
χ504-444-4-4-44-444-44-44-40000000000000000000000000000000000000000000000
χ514-44-4-444-4000000000022−2200−22220000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000000000000000
χ524-44-4-444-4000000000022−2200−22220000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000000000000000
χ534-44-4-444-40000000000−22220022−220000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000000000000000
χ544-44-4-444-40000000000−22220022−220000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000000000000000
χ554-4-444-44-40000000022−2200−222200000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000000
χ564-4-444-44-40000000022−2200−222200000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000000
χ574-4-444-44-400000000−22220022−2200000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000000
χ584-4-444-44-400000000−22220022−2200000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000000
χ594-4-4-444-444-44-400000000000000000000000000000000000000000000002i−2i−2i2i
χ604-4-4-444-444-44-40000000000000000000000000000000000000000000000−2i2i2i−2i
χ614-4-4-444-44-44-4400000000000000000000000000000000000000002-2-22000000
χ624-4-4-444-44-44-440000000000000000000000000000000000000000-222-2000000

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