Finite Group Databasebeta

← Group #138713

Character table — Group #138713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order12222244444488884448888888888888161616161616161644448888161616162444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ91111-1-1-1-111-1-1111111-1-1-1-1-11ii−i−iii−i−iiiii−i−i−i−i1-11-1ii−i−i11-1-11-1i−i
χ101111-1-1-1-111-1-1111111-1-1-1-1-11ii−i−iii−i−iiiii−i−i−i−i-11-11−i−iii11-1-1-11−ii
χ111111-1-1-1-111-1-1111111-1-1-1-1-11ii−i−iii−i−i−i−i−i−iiiii1-11-1ii−i−i-1-111-11−ii
χ121111-1-1-1-111-1-1111111-1-1-1-1-11ii−i−iii−i−i−i−i−i−iiiii-11-11−i−iii-1-1111-1i−i
χ131111-1-1-1-111-1-1111111-1-1-1-1-11−i−iii−i−iiiiiii−i−i−i−i1-11-1−i−iii-1-111-11i−i
χ141111-1-1-1-111-1-1111111-1-1-1-1-11−i−iii−i−iiiiiii−i−i−i−i-11-11ii−i−i-1-1111-1−ii
χ151111-1-1-1-111-1-1111111-1-1-1-1-11−i−iii−i−iii−i−i−i−iiiii1-11-1−i−iii11-1-11-1−ii
χ161111-1-1-1-111-1-1111111-1-1-1-1-11−i−iii−i−iii−i−i−i−iiiii-11-11ii−i−i11-1-1-11i−i
χ17222222222222-2-2-2-2222-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222222-2-22222-2-2-22-2-22-2000000000000000022-2-2000000000000
χ202222222222-2-22222-2-2-22-2-22-20000000000000000-2-222000000000000
χ212222222222-2-2-2-2-2-2-2-2-2-222-22000000000000000000002i−2i2i−2i00000000
χ222222222222-2-2-2-2-2-2-2-2-2-222-2200000000000000000000−2i2i−2i2i00000000
χ23222222-2-2-2-22200002-2-2000002-22-2000022−2−222−2−2000000002−22−20000
χ24222222-2-2-2-22200002-2-2000002-22-20000−2−222−2−22200000000−22−220000
χ25222222-2-2-2-22200002-2-200000-22-22000022−2−222−2−200000000−22−220000
χ26222222-2-2-2-22200002-2-200000-22-220000−2−222−2−222000000002−22−20000
χ272222-2-222-2-2-2-200002-22000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2000000002−2−220000
χ282222-2-222-2-2-2-200002-22000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i200000000−222−20000
χ292222-2-222-2-2-2-200002-2200000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i200000000−222−20000
χ302222-2-222-2-2-2-200002-2200000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2000000002−2−220000
χ312222-2-2-2-222222222-2-22-222-2-200000000000000002-2-22000000000000
χ322222-2-2-2-222222222-2-22-222-2-20000000000000000-222-2000000000000
χ332222-2-2-2-22222-2-2-2-2-2-222-2-222000000000000000000002-2-2200000000
χ342222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000-222-200000000
χ352222-2-2-2-222-2-2-2-2-2-222-22222-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-222-22222-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ37444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000
χ384444-4-444-4-4440000-44-40000000000000000000000000000000000000
χ394-44-40000004i−4i22−2222−2200002i2−2i20000000000ζ+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−ζ70000000000000000
χ404-44-40000004i−4i22−2222−2200002i2−2i20000000000−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+ζ70000000000000000
χ414-44-40000004i−4i−2222−22220000−2i22i20000000000ζ+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+ζ70000000000000000
χ424-44-40000004i−4i−2222−22220000−2i22i20000000000−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−ζ70000000000000000
χ434-44-4000000−4i4i22−2222−220000−2i22i20000000000ζ−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+ζ70000000000000000
χ444-44-4000000−4i4i22−2222−220000−2i22i20000000000−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−ζ70000000000000000
χ454-44-4000000−4i4i−2222−222200002i2−2i20000000000ζ−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−ζ70000000000000000
χ464-44-4000000−4i4i−2222−222200002i2−2i20000000000−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+ζ70000000000000000
χ474-4-444-44-44-40000000000000000002i2−2i22i2−2i2000000000000000000000000
χ484-4-444-44-44-4000000000000000000−2i22i2−2i22i2000000000000000000000000
χ494-4-444-4-44-440044-4-4000400-4000000000000000000000000000000000
χ504-4-444-4-44-4400-4-444000-4004000000000000000000000000000000000
χ514-4-44-444-4-440044-4-4000-4004000000000000000000000000000000000
χ524-4-44-444-4-4400-4-444000400-4000000000000000000000000000000000
χ534-4-44-44-444-400000000000000000022−22−2222000000000000000000000000
χ544-4-44-44-444-4000000000000000000−222222−22000000000000000000000000
χ5588-8-80000000042−42−42420000000000000000000000000000000000000000
χ5688-8-800000000−424242−420000000000000000000000000000000000000000

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