Finite Group Databasebeta

← Group #143556

Character table — Group #143556

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122222444444888844488888844448888161616161616161616161616161616168888244488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
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
χ1122222222-2-2220000-2-2-200000022-2-200002222−2−2−2−22222−2−2−2−20000000000
χ1222222222-2-2220000-2-2-200000022-2-20000−2−2−2−22222−2−2−2−222220000000000
χ1322222222-2-2220000-2-2-2000000-2-22200002222−2−2−2−2−2−2−2−222220000000000
χ1422222222-2-2220000-2-2-2000000-2-2220000−2−2−2−222222222−2−2−2−20000000000
χ15222222-2-222-2-22222-2-2222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ16222222-2-222-2-22222-2-2222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ17222222-2-222-2-2-2-2-2-2-2-22-2-22222000000000000000022-2-222-2-20000000000
χ18222222-2-222-2-2-2-2-2-2-2-22-2-222220000000000000000-2-222-2-2220000000000
χ19222222-2-2-2-2-2-2000022-200000000002i2i−2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000
χ20222222-2-2-2-2-2-2000022-200000000002i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000
χ21222222-2-2-2-2-2-2000022-20000000000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000
χ22222222-2-2-2-2-2-2000022-20000000000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000
χ232222-2-22-2222-222222-2-2-2-222-2-200000000000000000000000022-2-2000000
χ242222-2-22-2222-222222-2-2-2-222-2-2000000000000000000000000-2-222000000
χ252222-2-22-2222-2-2-2-2-22-2-222-2-2220000000000000000000000000000002-200
χ262222-2-22-2222-2-2-2-2-22-2-222-2-222000000000000000000000000000000-2200
χ272222-2-2-2222-222222-22-2-2-2-2-22200000000000000000000000000002-20000
χ282222-2-2-2222-222222-22-2-2-2-2-2220000000000000000000000000000-220000
χ292222-2-2-2222-22-2-2-2-2-22-22222-2-2000000000000000000000000000000002-2
χ302222-2-2-2222-22-2-2-2-2-22-22222-2-200000000000000000000000000000000-22
χ312-22-22-22-200-2222−2−20002−22−22−2002-22−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ70000000000
χ322-22-22-22-200-2222−2−20002−22−22−2002-22−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ70000000000
χ332-22-22-22-200-2222−2−20002−22−22−200-22−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ70000000000
χ342-22-22-22-200-2222−2−20002−22−22−200-22−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ70000000000
χ352-22-22-22-200-22−2−222000−22−22−22002-2−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ50000000000
χ362-22-22-22-200-22−2−222000−22−22−22002-2−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ50000000000
χ372-22-22-22-200-22−2−222000−22−22−2200-222−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ50000000000
χ382-22-22-22-200-22−2−222000−22−22−2200-222−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ50000000000
χ392-22-22-2-22002-222−2−20002−2−22−222i−2i00i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ50000000000
χ402-22-22-2-22002-222−2−20002−2−22−222i−2i00i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ50000000000
χ412-22-22-2-22002-222−2−20002−2−22−22−2i2i00−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ50000000000
χ422-22-22-2-22002-222−2−20002−2−22−22−2i2i00−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ50000000000
χ432-22-22-2-22002-2−2−222000−222−22−22i−2i00−i2i2i2−i2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ70000000000
χ442-22-22-2-22002-2−2−222000−222−22−22i−2i00−i2i2i2−i2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ70000000000
χ452-22-22-2-22002-2−2−222000−222−22−2−2i2i00i2−i2−i2i2ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ70000000000
χ462-22-22-2-22002-2−2−222000−222−22−2−2i2i00i2−i2−i2i2−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ70000000000
χ474444-4-44-4-4-44-40000-4440000000000000000000000000000000000000000
χ484444-4-4-44-4-4-4400004-440000000000000000000000000000000000000000
χ494-44-4-444400-4-42222−22−22000−222222−22−22220000000000000000000000000000000000
χ504-44-4-444400-4-4−22−22222200022−22−222222−220000000000000000000000000000000000
χ514-44-4-44-4-400442222−22−22000−2222−222222−220000000000000000000000000000000000
χ524-44-4-44-4-40044−22−22222200022−2222−22−22220000000000000000000000000000000000
χ534-4-4400004-4004-44-4000000000000000000000000000000000002i2−2i2000000
χ544-4-4400004-4004-44-400000000000000000000000000000000000−2i22i2000000
χ554-4-4400004-400-44-440000000000000000000000000000000002i2−2i200000000
χ564-4-4400004-400-44-44000000000000000000000000000000000−2i22i200000000
χ5788-8-80000000042−42−42420000000000000000000000000000000000000000000
χ5888-8-800000000−424242−420000000000000000000000000000000000000000000
χ598-8-880000-880000000000000000000000000000000000000000000000000

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