Finite Group Databasebeta

← Group #491251

Character table — Group #491251

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222444444444444444888888888888888888888816161616323232323232
order1222444488882444488161616161616161622448888881616161616161616161616168888244488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ4111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ9111111111111-11-1-1-111111111111-11-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11-11-11-1
χ10111111111111-11-1-1-111111111111-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-11-11-11
χ11111111111111-11-1-1-11111111111-11-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-11-111-1
χ12111111111111-11-1-1-11111111111-11-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-11-1-11
χ13111111111111-11-1-1-111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-1111111-1-1-111-1-11
χ14111111111111-11-1-1-111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-1-1-11111-1-1111-1-111-1
χ15111111111111-11-1-1-111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111111111-1-1-1-111-1-11-1-11-11
χ16111111111111-11-1-1-111-1-1-1-1-1-1-1-1-11-11-1-1-1-11111111111-1-1-1-1-1-111-111-11-1
χ1722222222-2-2-2-222222-2-2000000002222-2-2-2-2-2-20000000000000000000000
χ1822222222-2-2-2-222222-2-200000000-2-2-2-2-2-222220000000000000000000000
χ1922222222-2-2-2-2-22-2-2-2-2-2000000002-22-222-2-2220000000000000000000000
χ2022222222-2-2-2-2-22-2-2-2-2-200000000-22-222222-2-20000000000000000000000
χ21222222-2-222222-2-2-22-2-22222-2-2-2-20000-22000022-2-2000000000000000000
χ22222222-2-222222-2-2-22-2-2-2-2-2-222220000-220000-2-222000000000000000000
χ23222222-2-22222-2-222-2-2-22222-2-2-2-200002-20000-2-222000000000000000000
χ24222222-2-22222-2-222-2-2-2-2-2-2-2222200002-2000022-2-2000000000000000000
χ25222222-2-2-2-2-2-22-2-2-22220000000000002-2000000002i2i−2i−2i2i2i−2i−2i0000000000
χ26222222-2-2-2-2-2-22-2-2-22220000000000002-200000000−2i−2i2i2i−2i−2i2i2i0000000000
χ27222222-2-2-2-2-2-2-2-222-222000000000000-22000000002i2i−2i−2i−2i−2i2i2i0000000000
χ28222222-2-2-2-2-2-2-2-222-222000000000000-2200000000−2i−2i2i2i2i2i−2i−2i0000000000
χ292222-2-22200002-2-22-20022−2−222−2−22-2-220000002−22−22−22−22−22−20000000000
χ302222-2-22200002-2-22-20022−2−222−2−2-222-20000002−22−2−22−22−22−220000000000
χ312222-2-22200002-2-22-200−2−222−2−2222-2-22000000−22−22−22−22−22−220000000000
χ322222-2-22200002-2-22-200−2−222−2−222-222-2000000−22−222−22−22−22−20000000000
χ332222-2-2220000-2-22-220022−2−222−2−222-2-2000000−22−222−22−2−22−220000000000
χ342222-2-2220000-2-22-220022−2−222−2−2-2-222000000−22−22−22−222−22−20000000000
χ352222-2-2220000-2-22-2200−2−222−2−22222-2-20000002−22−2−22−222−22−20000000000
χ362222-2-2220000-2-22-2200−2−222−2−222-2-2220000002−22−22−22−2−22−220000000000
χ372222-2-2-2-20000222-2-20022−2−2−2−2220000002i−2i2i−2i2−2−22i2−i2−i2i2i2−i2−i2i20000000000
χ382222-2-2-2-20000222-2-20022−2−2−2−222000000−2i2i−2i2i2−2−22−i2i2i2−i2−i2i2i2−i20000000000
χ392222-2-2-2-20000222-2-200−2−22222−2−20000002i−2i2i−2i−222−2−i2i2i2−i2−i2i2i2−i20000000000
χ402222-2-2-2-20000222-2-200−2−22222−2−2000000−2i2i−2i2i−222−2i2−i2−i2i2i2−i2−i2i20000000000
χ412222-2-2-2-20000-22-2220022−2−2−2−2220000002i−2i−2i2i−222−2i2−i2−i2i2−i2i2i2−i20000000000
χ422222-2-2-2-20000-22-2220022−2−2−2−222000000−2i2i2i−2i−222−2−i2i2i2−i2i2−i2−i2i20000000000
χ432222-2-2-2-20000-22-22200−2−22222−2−20000002i−2i−2i2i2−2−22−i2i2i2−i2i2−i2−i2i20000000000
χ442222-2-2-2-20000-22-22200−2−22222−2−2000000−2i2i2i−2i2−2−22i2−i2−i2i2−i2i2i2−i20000000000
χ454-44-4004-42222−22−220000022−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ464-44-4004-42222−22−220000022−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ474-44-4004-4−22−22222200000−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ484-44-4004-4−22−22222200000−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ494-44-400-442222−22−2200000−22222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000
χ504-44-400-442222−22−2200000−2222−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000
χ514-44-400-44−22−2222220000022−222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000
χ524-44-400-44−22−2222220000022−22−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000
χ534-4-44-44004-44-4000000000000000000000000000000000000022−2200000000
χ544-4-44-44004-44-40000000000000000000000000000000000000−222200000000
χ554-4-44-4400-44-4400000000000000000000000000000000000000022−22000000
χ564-4-44-4400-44-44000000000000000000000000000000000000000−2222000000
χ5788-8-8000042−42−424200000000000000000000000000000000000000000000000
χ5888-8-80000−424242−4200000000000000000000000000000000000000000000000
χ598-8-888-800000000000000000000000000000000000000000000000000000

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