Finite Group Databasebeta

← Group #144591

Character table — Group #144591

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122222222244888844488888844448888161616161616161616161616161616164444244444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ9222222222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000
χ10222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ112222222222-2-20000-2-2-200000022-2-200002222−2−2−2−22222−2−2−2−20000000000
χ122222222222-2-20000-2-2-200000022-2-20000−2−2−2−22222−2−2−2−222220000000000
χ132222222222-2-20000-2-2-2000000-2-22200002222−2−2−2−2−2−2−2−222220000000000
χ142222222222-2-20000-2-2-2000000-2-2220000−2−2−2−222222222−2−2−2−20000000000
χ15222222-2-2-2-22222222-2-2-2-2-2-2220000000000000000000000000000002i−2i00
χ16222222-2-2-2-22222222-2-2-2-2-2-222000000000000000000000000000000−2i2i00
χ17222222-2-2-2-222-2-2-2-22-2-22222-2-200000000000000000000000000002-20000
χ18222222-2-2-2-222-2-2-2-22-2-22222-2-20000000000000000000000000000-220000
χ192222-2-22-22-2222222-22-222-2-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ202222-2-22-22-2222222-22-222-2-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ212222-2-22-22-222-2-2-2-2-22-2-2-22222000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ222222-2-22-22-222-2-2-2-2-22-2-2-2222200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ232222-2-22-22-2-2-200002-22000000000022-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ242222-2-22-22-2-2-200002-22000000000022-2-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ252222-2-22-22-2-2-200002-220000000000-2-222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000
χ262222-2-22-22-2-2-200002-220000000000-2-222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000
χ272222-2-2-22-22222222-2-22-2-222-2-2000000000000000000000000000000002-2
χ282222-2-2-22-22222222-2-22-2-222-2-200000000000000000000000000000000-22
χ292222-2-2-22-2222-2-2-2-2-2-2222-2-22200000000000000000000000022-2-2000000
χ302222-2-2-22-2222-2-2-2-2-2-2222-2-222000000000000000000000000-2-222000000
χ312-2-222-2-222-20022−2−20002−22−22−22-2002−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ50000000000
χ322-2-222-2-222-20022−2−20002−22−22−22-2002−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ50000000000
χ332-2-222-2-222-20022−2−20002−22−22−2-2200−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ50000000000
χ342-2-222-2-222-20022−2−20002−22−22−2-2200−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ50000000000
χ352-2-222-2-222-200−2−222000−22−22−222-200−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ70000000000
χ362-2-222-2-222-200−2−222000−22−22−222-200−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ70000000000
χ372-2-222-2-222-200−2−222000−22−22−22-22002−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ70000000000
χ382-2-222-2-222-200−2−222000−22−22−22-22002−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ70000000000
χ392-2-22-22-2-2220022−2−20002−2−22−22002-22−2−22ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ70000000000
χ402-2-22-22-2-2220022−2−20002−2−22−22002-22−2−22−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ70000000000
χ412-2-22-22-2-2220022−2−20002−2−22−2200-22−222−2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ70000000000
χ422-2-22-22-2-2220022−2−20002−2−22−2200-22−222−2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ70000000000
χ432-2-22-22-2-22200−2−222000−222−22−2002-2−222−2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ50000000000
χ442-2-22-22-2-22200−2−222000−222−22−2002-2−222−2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ50000000000
χ452-2-22-22-2-22200−2−222000−222−22−200-222−2−22ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ50000000000
χ462-2-22-22-2-22200−2−222000−222−22−200-222−2−22−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ50000000000
χ47444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000
χ484444-4-4-44-44-4-4000044-40000000000000000000000000000000000000000
χ494-44-40000004-44i−4i4i−4i0000000000000000000000000000000002-22i−2i000000
χ504-44-40000004-44i−4i4i−4i000000000000000000000000000000000-22−2i2i000000
χ514-44-40000004-4−4i4i−4i4i0000000000000000000000000000000002-2−2i2i000000
χ524-44-40000004-4−4i4i−4i4i000000000000000000000000000000000-222i−2i000000
χ534-4-444-44-4-44002222−22−22000−2222−222222−220000000000000000000000000000000000
χ544-4-444-44-4-4400−22−22222200022−2222−22−22220000000000000000000000000000000000
χ554-4-44-4444-4-4002222−22−22000−222222−22−22220000000000000000000000000000000000
χ564-4-44-4444-4-400−22−22222200022−22−222222−220000000000000000000000000000000000
χ5788-8-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000
χ5888-8-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000
χ598-88-8000000-8800000000000000000000000000000000000000000000000

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