Finite Group Databasebeta

← Group #151636

Character table — Group #151636

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11222222222222222444444444444444444444444161616161616161616161616161616166464
order1224488881616161616161616448888888888161616161616161616161616248816161616323232323232323224
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1
χ6111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11
χ7111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ8111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1
χ92222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-222-2-2-2-22222000000000000000000
χ10222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000
χ112222222-2-200002222-2-2000000002-22200-2-2-2-2000022-2-200000000000000
χ122222222-2-200002222-2-2000000002-22200-2-2-2-20000-2-22200000000000000
χ132222222-2-20000-2-2-2-2-2-2000000002-2-2-2002222000000002i2i−2i−2i0000000000
χ142222222-2-20000-2-2-2-2-2-2000000002-2-2-200222200000000−2i−2i2i2i0000000000
χ1522222-2-22222220000-2-200000000-2200220000-2-2-2-20000000022−2−222−2−200
χ1622222-2-22222220000-2-200000000-2200220000-2-2-2-200000000−2−222−2−22200
χ1722222-2-222-2-2-2-20000-2-200000000-2200-2-2000022220000000022−2−2−2−22200
χ1822222-2-222-2-2-2-20000-2-200000000-2200-2-20000222200000000−2−22222−2−200
χ1922-22-2220022−2−22222002222−2−2−2−2-20-2-22−2000022−2−22-2002−22−20000000000
χ2022-22-2220022−2−22222002222−2−2−2−2-20-2-22−2000022−2−2-2200−22−220000000000
χ2122-22-2220022−2−2-2-2-2-200−2−2−2−22222-20222−2000022−2−2002i−2ii2−i2−i2i20000000000
χ2222-22-2220022−2−2-2-2-2-200−2−2−2−22222-20222−2000022−2−200−2i2i−i2i2i2−i20000000000
χ2322-22-22200−2−222222200−2−2−2−22222-20-2-2−220000−2−2222-200−22−220000000000
χ2422-22-22200−2−222222200−2−2−2−22222-20-2-2−220000−2−222-22002−22−20000000000
χ2522-22-22200−2−222-2-2-2-2002222−2−2−2−2-2022−220000−2−222002i−2i−i2i2i2−i20000000000
χ2622-22-22200−2−222-2-2-2-2002222−2−2−2−2-2022−220000−2−22200−2i2ii2−i2−i2i20000000000
χ2722-2-220022222222−2−20022−2−222−2−20-22−2-2-222−2−2000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500
χ2822-2-220022222222−2−20022−2−222−2−20-22−2-2-222−2−2000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500
χ2922-2-2200222222−2−22200−2−222−2−2220-2−22-2-2−2−222000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700
χ3022-2-2200222222−2−22200−2−222−2−2220-2−22-2-2−2−222000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700
χ3122-2-220022-2-2-2-222−2−200−2−222−2−2220-22−22222−2−2000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ500
χ3222-2-220022-2-2-2-222−2−200−2−222−2−2220-22−22222−2−2000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ500
χ3322-2-220022-2-2-2-2−2−2220022−2−222−2−20-2−2222−2−222000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ700
χ3422-2-220022-2-2-2-2−2−2220022−2−222−2−20-2−2222−2−222000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ700
χ3544444-4-4-4-4000000004400000000-4-4000000000000000000000000000000
χ36444-4-400002222−22−222222−22−220022-2-2-2-22200−2222−222200000000000000000000000000
χ37444-4-400002222−22−22−22−22222200-2-22222-2-20022−22−222200000000000000000000000000
χ38444-4-40000−22−2222222222−22−2200-2-22222-2-200−222222−2200000000000000000000000000
χ39444-4-40000−22−222222−22−2222220022-2-2-2-2220022−2222−2200000000000000000000000000
χ4044-44-4-4-4002222−22−2200000000000000400022−220000−22−222222000000000000000000
χ4144-44-4-4-400−22−222222000000000000004000−222200002222−22−22000000000000000000
χ4244-4-4400-4-400002222−22−2200000000000422−2200−22−2222220000000000000000000000
χ4344-4-4400-4-40000−22−222222000000000004−2222002222−22−220000000000000000000000
χ444-400022−2222−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-2i2−i2ζ2−2i+ζ6−ζ2+2i−ζ6ζ2+2i+ζ6−ζ2−2i−ζ6i2−i2000000ζ+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
χ454-400022−2222−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-2−i2i2−ζ2+2i−ζ6ζ2−2i+ζ6−ζ2−2i−ζ6ζ2+2i+ζ6−i2i2000000−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
χ464-400022−2222−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52-2−i2i2−ζ2+2i−ζ6ζ2−2i+ζ6−ζ2−2i−ζ6ζ2+2i+ζ6−i2i2000000ζ+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
χ474-400022−2222−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52-2i2−i2ζ2−2i+ζ6−ζ2+2i−ζ6ζ2+2i+ζ6−ζ2−2i−ζ6i2−i2000000−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
χ484-400022−22−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-22ζ2+2i+ζ6−ζ2−2i−ζ6−i2i2−i2i2ζ2−2i+ζ6−ζ2+2i−ζ6000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000000
χ494-400022−22−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-22−ζ2−2i−ζ6ζ2+2i+ζ6i2−i2i2−i2−ζ2+2i−ζ6ζ2−2i+ζ6000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000000
χ504-400022−22−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5-22−ζ2−2i−ζ6ζ2+2i+ζ6i2−i2i2−i2−ζ2+2i−ζ6ζ2−2i+ζ6000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000000
χ514-400022−22−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5-22ζ2+2i+ζ6−ζ2−2i−ζ6−i2i2−i2i2ζ2−2i+ζ6−ζ2+2i−ζ6000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000000
χ524-4000−222222−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-22−ζ2+2i−ζ6ζ2−2i+ζ6i2−i2i2−i2−ζ2−2i−ζ6ζ2+2i+ζ6000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000000
χ534-4000−222222−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-22ζ2−2i+ζ6−ζ2+2i−ζ6−i2i2−i2i2ζ2+2i+ζ6−ζ2−2i−ζ6000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000000
χ544-4000−222222−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7-22ζ2−2i+ζ6−ζ2+2i−ζ6−i2i2−i2i2ζ2+2i+ζ6−ζ2−2i−ζ6000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000000
χ554-4000−222222−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7-22−ζ2+2i−ζ6ζ2−2i+ζ6i2−i2i2−i2−ζ2−2i−ζ6ζ2+2i+ζ6000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000000
χ564-4000−2222−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-2i2−i2ζ2+2i+ζ6−ζ2−2i−ζ6ζ2−2i+ζ6−ζ2+2i−ζ6i2−i2000000−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
χ574-4000−2222−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-2−i2i2−ζ2−2i−ζ6ζ2+2i+ζ6−ζ2+2i−ζ6ζ2−2i+ζ6−i2i2000000ζ−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
χ584-4000−2222−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72-2−i2i2−ζ2−2i−ζ6ζ2+2i+ζ6−ζ2+2i−ζ6ζ2−2i+ζ6−i2i2000000−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
χ594-4000−2222−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ72-2i2−i2ζ2+2i+ζ6−ζ2−2i−ζ6ζ2−2i+ζ6−ζ2+2i−ζ6i2−i2000000ζ−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

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