Finite Group Databasebeta

← Group #136151

Character table — Group #136151

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order122244442244224488888888888816161616161616161616161616161616244444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1-1-1111-1-1111-1-111-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1i−ii−ii−iii−i−i11-1-1
χ101111-1-1-1-1-1-1111-1-1111-1-111-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1-1-111i−i−ii−ii−i−iii-1-111
χ111111-1-1-1-1-1-1111-1-1111-1-111-1-1ii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1i−ii−ii−i−i−iii-1-111
χ121111-1-1-1-1-1-1111-1-1111-1-111-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111-1-111i−i−ii−iiii−i−i11-1-1
χ131111-1-1-1-1-1-1111-1-1111-1-111-1-1−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1−ii−ii−iiii−i−i-1-111
χ141111-1-1-1-1-1-1111-1-1111-1-111-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111-1-111−iii−ii−i−i−iii11-1-1
χ151111-1-1-1-1-1-1111-1-1111-1-111-1-1−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1−ii−ii−ii−i−iii11-1-1
χ161111-1-1-1-1-1-1111-1-1111-1-111-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1-1-111−iii−ii−iii−i−i-1-111
χ172222222222222222-2-2-2-2-2-2-2-2222200000000000000000000-2-2000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022000000000000
χ19222222222222-2-2-2-222-2-2-2-222000000000000000000002-2-2200000000000000
χ20222222222222-2-2-2-222-2-2-2-22200000000000000000000-222-200000000000000
χ21222222222222-2-2-2-2-2-22222-2-20000000000000000000000000022-2-200000000
χ22222222222222-2-2-2-2-2-22222-2-200000000000000000000000000-2-22200000000
χ2322222222-2-2-2-2-22-22000000002-22-222−2−222−2−222−2−222−2−2000000000000000000
χ2422222222-2-2-2-2-22-22000000002-22-2−2−222−2−222−2−222−2−222000000000000000000
χ2522222222-2-2-2-2-22-2200000000-22-2222−2−222−2−2−2−222−2−222000000000000000000
χ2622222222-2-2-2-2-22-2200000000-22-22−2−222−2−22222−2−222−2−2000000000000000000
χ272222-2-2-2-222-2-2-2-222000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000
χ282222-2-2-2-222-2-2-2-222000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000
χ292222-2-2-2-222-2-2-2-22200000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000000000
χ302222-2-2-2-222-2-2-2-22200000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000000000
χ312222-2-2-2-2-2-2222-2-22-2-222-2-2222i2i−2i−2i00000000000000000000−2i2i000000000000
χ322222-2-2-2-2-2-2222-2-22-2-222-2-222−2i−2i2i2i000000000000000000002i−2i000000000000
χ332222-2-2-2-2-2-222-222-22222-2-2-2-2000000000000000000002-22-200000000000000
χ342222-2-2-2-2-2-222-222-22222-2-2-2-200000000000000000000-22-2200000000000000
χ352222-2-2-2-2-2-222-222-2-2-2-2-22222000000000000000000000000002i−2i−2i2i00000000
χ362222-2-2-2-2-2-222-222-2-2-2-2-2222200000000000000000000000000−2i2i2i−2i00000000
χ3744444444-4-4-4-44-44-40000000000000000000000000000000000000000000000
χ384444-4-4-4-444-4-444-4-40000000000000000000000000000000000000000000000
χ3944-4-44i−4i4i−4i00000000002i2−2i222−22000000ζ+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
χ4044-4-44i−4i4i−4i00000000002i2−2i222−22000000−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
χ4144-4-44i−4i4i−4i0000000000−2i22i2−2222000000ζ+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
χ4244-4-44i−4i4i−4i0000000000−2i22i2−2222000000−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
χ4344-4-4−4i4i−4i4i00000000002i2−2i2−2222000000ζ−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
χ4444-4-4−4i4i−4i4i00000000002i2−2i2−2222000000−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
χ4544-4-4−4i4i−4i4i0000000000−2i22i222−22000000ζ−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
χ4644-4-4−4i4i−4i4i0000000000−2i22i222−22000000−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
χ474-44-44i−4i−4i4i0000000022−2200002i2−2i2000000000000ζ+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
χ484-44-44i−4i−4i4i0000000022−2200002i2−2i2000000000000−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
χ494-44-44i−4i−4i4i00000000−22220000−2i22i2000000000000ζ−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
χ504-44-44i−4i−4i4i00000000−22220000−2i22i2000000000000−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
χ514-44-4−4i4i4i−4i0000000022−220000−2i22i2000000000000ζ+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
χ524-44-4−4i4i4i−4i0000000022−220000−2i22i2000000000000−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
χ534-44-4−4i4i4i−4i00000000−222200002i2−2i2000000000000ζ−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
χ544-44-4−4i4i4i−4i00000000−222200002i2−2i2000000000000−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
χ554-4-4444-4-44-44-400000000000000000000000000000000000000000000002-22-2
χ564-4-4444-4-44-44-40000000000000000000000000000000000000000000000-22-22
χ574-4-4444-4-4-44-440000000000000000000000000000000000000000002i−2i2i−2i0000
χ584-4-4444-4-4-44-44000000000000000000000000000000000000000000−2i2i−2i2i0000
χ594-4-44-4-4444-4-440000000000000000000000000000000000000000002-2-220000
χ604-4-44-4-4444-4-44000000000000000000000000000000000000000000-222-20000
χ614-4-44-4-444-444-400000000000000000000000000000000000000000000002-2-22
χ624-4-44-4-444-444-40000000000000000000000000000000000000000000000-222-2

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