Finite Group Databasebeta

← Group #131639

Character table — Group #131639

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222444444444888888888888816161616161616161616161616161616161616161616
order12224444444424488888824448161616161616161624444444888888888816161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111
χ91111-1-11111-1-11-1-111-1-1-1-11-11-11iiii−i−i−i−i11-1-111-1-11-1ii−i−iii−i−iii−i−i
χ101111-1-11111-1-11-1-111-1-1-1-11-11-11iiii−i−i−i−i-1-111-1-1111-1−i−iii−i−iiiii−i−i
χ111111-1-11111-1-11-1-111-1-1-1-11-11-11−i−i−i−iiiii11-1-111-1-11-1−i−iii−i−iii−i−iii
χ121111-1-11111-1-11-1-111-1-1-1-11-11-11−i−i−i−iiiii-1-111-1-1111-1ii−i−iii−i−i−i−iii
χ131111-1-11111-1-11-1-111-1-1-1-1-11-111iiii−i−i−i−i11-1-1-1-111-11ii−i−i−i−iii−i−iii
χ141111-1-11111-1-11-1-111-1-1-1-1-11-111iiii−i−i−i−i-1-11111-1-1-11−i−iiiii−i−i−i−iii
χ151111-1-11111-1-11-1-111-1-1-1-1-11-111−i−i−i−iiiii11-1-1-1-111-11−i−iiiii−i−iii−i−i
χ161111-1-11111-1-11-1-111-1-1-1-1-11-111−i−i−i−iiiii-1-11111-1-1-11ii−i−i−i−iiiii−i−i
χ17222222222222222-2-2-2-2-2-22222-20000000000000000-2-2000000000000
χ18222222222222222-2-2-2-2-2-2-2-2-2-2-2000000000000000022000000000000
χ19222222-2-22222-2-2-22222-2-20000-2000000002-22-2000000000000000000
χ20222222-2-22222-2-2-22222-2-20000-200000000-22-22000000000000000000
χ21222222-2-22222-2-2-2-2-2-2-222000020000000000002-22-200000000000000
χ22222222-2-22222-2-2-2-2-2-2-22200002000000000000-22-2200000000000000
χ23222222-2-2-2-2-2-222-20000002-2-220i2i2−i2−i2i2i2−i2−i2000000000000000000i2−i2i2−i2
χ24222222-2-2-2-2-2-222-20000002-2-220−i2−i2i2i2−i2−i2i2i2000000000000000000−i2i2−i2i2
χ25222222-2-2-2-2-2-222-2000000-222-20i2i2−i2−i2i2i2−i2−i2000000000000000000−i2i2−i2i2
χ26222222-2-2-2-2-2-222-2000000-222-20−i2−i2i2i2−i2−i2i2i2000000000000000000i2−i2i2−i2
χ272222-2-22222-2-22-2-2-2-222222-22-2-20000000000000000-22000000000000
χ282222-2-22222-2-22-2-2-2-22222-22-22-200000000000000002-2000000000000
χ292222-2-2-2-222-2-2-22222-2-2220000-2000000002-2-22000000000000000000
χ302222-2-2-2-222-2-2-22222-2-2220000-200000000-222-2000000000000000000
χ312222-2-2-2-222-2-2-222-2-222-2-2000020000000000002-2-2200000000000000
χ322222-2-2-2-222-2-2-222-2-222-2-200002000000000000-222-200000000000000
χ332222-2-2-2-2-2-2222-2200000022-2-2022−2−2−2−2220000000000000000002−2−22
χ342222-2-2-2-2-2-2222-2200000022-2-20−2−22222−2−2000000000000000000−222−2
χ352222-2-2-2-2-2-2222-22000000-2-222022−2−2−2−222000000000000000000−222−2
χ362222-2-2-2-2-2-2222-22000000-2-2220−2−22222−2−20000000000000000002−2−22
χ3744444444-4-4-4-4-4-4400000000000000000000000000000000000000000
χ384444-4-444-4-444-44-400000000000000000000000000000000000000000
χ394-44-4004i−4i00000000022−222i2−2i2000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ70000000000000000000000
χ404-44-4004i−4i00000000022−222i2−2i200000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ70000000000000000000000
χ414-44-4004i−4i000000000−2222−2i22i2000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ30000000000000000000000
χ424-44-4004i−4i000000000−2222−2i22i200000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ30000000000000000000000
χ434-44-400−4i4i00000000022−22−2i22i2000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ0000000000000000000000
χ444-44-400−4i4i00000000022−22−2i22i200000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ0000000000000000000000
χ454-44-400−4i4i000000000−22222i2−2i2000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ50000000000000000000000
χ464-44-400−4i4i000000000−22222i2−2i200000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ50000000000000000000000
χ474-4-444i−4i004-44i−4i000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ600000000
χ484-4-444i−4i004-44i−4i00000000000000000000000000000000−2ζ22ζ2−2ζ62ζ600000000
χ494-4-444i−4i00-44−4i4i0000000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ20000
χ504-4-444i−4i00-44−4i4i000000000000000000000000000000000000−2ζ62ζ6−2ζ22ζ20000
χ514-4-44−4i4i004-4−4i4i000000000000000000000000000000002ζ6−2ζ62ζ2−2ζ200000000
χ524-4-44−4i4i004-4−4i4i00000000000000000000000000000000−2ζ62ζ6−2ζ22ζ200000000
χ534-4-44−4i4i00-444i−4i0000000000000000000000000000000000002ζ2−2ζ22ζ6−2ζ60000
χ544-4-44−4i4i00-444i−4i000000000000000000000000000000000000−2ζ22ζ2−2ζ62ζ60000
χ5588-8-80000000000042−42000000000000000000000000000000000000000
χ5688-8-800000000000−4242000000000000000000000000000000000000000

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