Finite Group Databasebeta

← Group #145149

Character table — Group #145149

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order122222444444888844488888161616161616161616161616161616162224448888884488
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-1
χ9222222222222-2-2-2-2222-2-2-2-2-200000000000000002002000000-2-20000
χ10222222222222-2-2-2-2222-2-2-2-2-20000000000000000-200-2000000220000
χ1122222222-2-2222222-2-2-222-2-2-200000000000000000220-2-20000000000
χ1222222222-2-2222222-2-2-222-2-2-200000000000000000-2-20220000000000
χ1322222222-2-222-2-2-2-2-2-2-2-2-22220000000000000000000000000000002-2
χ1422222222-2-222-2-2-2-2-2-2-2-2-2222000000000000000000000000000000-22
χ15222222-2-2-2-2-2-2000022-2000002222−2−2−2−2i2i2i2i2−i2−i2−i2−i200000000002i−2i0000
χ16222222-2-2-2-2-2-2000022-2000002222−2−2−2−2−i2−i2−i2−i2i2i2i2i20000000000−2i2i0000
χ17222222-2-2-2-2-2-2000022-200000−2−2−2−22222i2i2i2i2−i2−i2−i2−i20000000000−2i2i0000
χ18222222-2-2-2-2-2-2000022-200000−2−2−2−22222−i2−i2−i2−i2i2i2i2i200000000002i−2i0000
χ192222-2-22-2-2-2-2200002-2200000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2200-2000000000000
χ202222-2-22-2-2-2-2200002-2200000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-2002000000000000
χ212222-2-22-2-2-2-2200002-2200000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-2002000000000000
χ222222-2-22-2-2-2-2200002-2200000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2200-2000000000000
χ232222-2-2-22222-222222-2-2-2-222-20000000022-2-2-2-2220000000000000000
χ242222-2-2-22222-222222-2-2-2-222-200000000-2-22222-2-20000000000000000
χ252222-2-2-22222-2-2-2-2-22-2-222-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ262222-2-2-22222-2-2-2-2-22-2-222-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ272222-2-2-22-2-22-22222-222-2-2-2-2200000000000000000000002i2i−2i−2i000000
χ282222-2-2-22-2-22-22222-222-2-2-2-220000000000000000000000−2i−2i2i2i000000
χ292222-2-2-22-2-22-2-2-2-2-2-2222222-200000000000000000000000000002i−2i00
χ302222-2-2-22-2-22-2-2-2-2-2-2222222-20000000000000000000000000000−2i2i00
χ312-22-22-22-2002-2-2-2220002-2000000000002−22−22−22−200002i−2ii2−i2i2−i2000000
χ322-22-22-22-2002-2-2-2220002-2000000000002−22−22−22−20000−2i2i−i2i2−i2i2000000
χ332-22-22-22-2002-2-2-2220002-200000000000−22−22−22−2200002i−2i−i2i2−i2i2000000
χ342-22-22-22-2002-2-2-2220002-200000000000−22−22−22−220000−2i2ii2−i2i2−i2000000
χ352-22-2-22-2-20022-2-222000-22000000000002−2−22−222−202-20002−2−22000000
χ362-22-2-22-2-20022-2-222000-22000000000002−2−22−222−20-22000−222−2000000
χ372-22-2-22-2-20022-2-222000-2200000000000−222−22−2−2202-2000−222−2000000
χ382-22-2-22-2-20022-2-222000-2200000000000−222−22−2−220-220002−2−22000000
χ39444444-4-444-4-40000-4-440000000000000000000000000000000000000
χ404444-4-44-444-440000-44-40000000000000000000000000000000000000
χ4144-4-400004i−4i0022−2222−22000002i2−2i202ζ−2ζ2ζ7−2ζ72ζ3−2ζ32ζ5−2ζ5000000000000000000000000
χ4244-4-400004i−4i0022−2222−22000002i2−2i20−2ζ2ζ−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5000000000000000000000000
χ4344-4-400004i−4i00−2222−222200000−2i22i202ζ5−2ζ52ζ3−2ζ3−2ζ72ζ7−2ζ2ζ000000000000000000000000
χ4444-4-400004i−4i00−2222−222200000−2i22i20−2ζ52ζ5−2ζ32ζ32ζ7−2ζ72ζ−2ζ000000000000000000000000
χ4544-4-40000−4i4i0022−2222−2200000−2i22i202ζ7−2ζ72ζ−2ζ2ζ5−2ζ52ζ3−2ζ3000000000000000000000000
χ4644-4-40000−4i4i0022−2222−2200000−2i22i20−2ζ72ζ7−2ζ2ζ−2ζ52ζ5−2ζ32ζ3000000000000000000000000
χ4744-4-40000−4i4i00−2222−2222000002i2−2i202ζ3−2ζ32ζ5−2ζ5−2ζ2ζ−2ζ72ζ7000000000000000000000000
χ4844-4-40000−4i4i00−2222−2222000002i2−2i20−2ζ32ζ3−2ζ52ζ52ζ−2ζ2ζ7−2ζ7000000000000000000000000
χ494-44-44-44-4004-444-4-4000-4400000000000000000000000000000000000
χ504-44-44-4-4400-44000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ514-44-44-4-4400-4400000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ524-44-4-444400-4-4000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ534-44-4-444400-4-400000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ544-44-4-44-4-4004444-4-40004-400000000000000000000000000000000000
χ558-8-880000000042−42−42420000000000000000000000000000000000000000
χ568-8-8800000000−424242−420000000000000000000000000000000000000000

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