Finite Group Databasebeta

← Group #145268

Character table — Group #145268

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222224444444444444444444444444416161616161616163232323232323232
order1222444444888824448888881616161616161616161616161616161624881616161624888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ92222222222-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-2000000000000
χ102222222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2-222000000000000
χ11222222-2-2220000-2-22-200000022222222−2−2−2−2−2−2−2−22-20022−2−200000000
χ12222222-2-2220000-2-22-200000022222222−2−2−2−2−2−2−2−2-2200−2−22200000000
χ13222222-2-2220000-2-22-2000000−2−2−2−2−2−2−2−2222222222-200−2−22200000000
χ14222222-2-2220000-2-22-2000000−2−2−2−2−2−2−2−222222222-220022−2−200000000
χ1522222-222-222222-2-2-2222-2-2-2-20000000000000000000000002-2000000
χ1622222-222-222222-2-2-2222-2-2-2-2000000000000000000000000-22000000
χ1722222-222-22-2-2-2-2-2-2-22-2-2222200000000000000000000000000002-200
χ1822222-222-22-2-2-2-2-2-2-22-2-222220000000000000000000000000000-2200
χ192222-22222-22222-22-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000
χ202222-22222-22222-22-2-2-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000
χ212222-22222-2-2-2-2-2-22-2-22222-2-2000000000000000000002i−2i2i−2i00000000
χ222222-22222-2-2-2-2-2-22-2-22222-2-200000000000000000000−2i2i−2i2i00000000
χ232222-22-2-22-200002-2-220000002222−2−2−2−2−2−2−2−22222002i−2ii2−i2−i2i200000000
χ242222-22-2-22-200002-2-220000002222−2−2−2−2−2−2−2−2222200−2i2i−i2i2i2−i200000000
χ252222-22-2-22-200002-2-22000000−2−2−2−222222222−2−2−2−2002i−2i−i2i2i2−i200000000
χ262222-22-2-22-200002-2-22000000−2−2−2−222222222−2−2−2−200−2i2ii2−i2−i2i200000000
χ272222-2-222-2-222222-22-2-2-222-2-2000000000000000000000000002i−2i0000
χ282222-2-222-2-222222-22-2-2-222-2-200000000000000000000000000−2i2i0000
χ292222-2-222-2-2-2-2-2-22-22-222-2-2220000000000000000000000000000002i−2i
χ302222-2-222-2-2-2-2-2-22-22-222-2-222000000000000000000000000000000−2i2i
χ3144444-4-4-4-44000044-4-400000000000000000000000000000000000000
χ324444-4-4-4-4-4-40000-444400000000000000000000000000000000000000
χ3344-4-440000-422−2222−22000022−220000ζ+ζ3−ζ5−ζ7ζ+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−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ70000000000000000
χ3444-4-440000-422−2222−22000022−220000−ζ−ζ3+ζ5+ζ7−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+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ70000000000000000
χ3544-4-440000-4−2222−22220000−22220000ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+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−ζ7ζ+ζ3−ζ5−ζ70000000000000000
χ3644-4-440000-4−2222−22220000−22220000−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−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+ζ7−ζ−ζ3+ζ5+ζ70000000000000000
χ3744-4-4-40000422−2222−220000−22220000ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ70000000000000000
χ3844-4-4-40000422−2222−220000−22220000−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ70000000000000000
χ3944-4-4-400004−2222−2222000022−220000ζ−ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ+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−ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ70000000000000000
χ4044-4-4-400004−2222−2222000022−220000−ζ+ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ−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+ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ70000000000000000
χ414-44-4004-40000000000004i−4i002-22-22i−2i2i−2i2-22-22i−2i2i−2i0000000000000000
χ424-44-4004-40000000000004i−4i00-22-22−2i2i−2i2i-22-22−2i2i−2i2i0000000000000000
χ434-44-4004-4000000000000−4i4i002-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000
χ444-44-4004-4000000000000−4i4i00-22-222i−2i2i−2i-22-222i−2i2i−2i0000000000000000
χ454-44-400-440044-4-4000000000000002i2−2i22i2−2i20000−2i22i2−2i22i20000000000000000
χ464-44-400-440044-4-400000000000000−2i22i2−2i22i200002i2−2i22i2−2i20000000000000000
χ474-44-400-4400-4-444000000000022−2222−220000−2222−222200000000000000000000
χ484-44-400-4400-4-4440000000000−2222−2222000022−2222−2200000000000000000000
χ494-4-440400-4022−22−22220000000022−2200002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ50000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ70000000000000000
χ504-4-440400-4022−22−22220000000022−220000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ70000000000000000
χ514-4-440400-40−222222−2200000000−222200002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ50000000000000000
χ524-4-440400-40−222222−2200000000−22220000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ70000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ50000000000000000
χ534-4-440-4004022−22−222200000000−22222ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000
χ544-4-440-4004022−22−222200000000−2222−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000
χ554-4-440-40040−222222−220000000022−222ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000
χ564-4-440-40040−222222−220000000022−22−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000

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