Finite Group Databasebeta

← Group #143648

Character table — Group #143648

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122222444444888844488888888888888161616161616161616161616161616164444244444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-11
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1
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
χ15222222-2-222-2-222222-2-222-2-2-2-20000000022-2-222-2-2000000000000000000
χ16222222-2-222-2-222222-2-222-2-2-2-200000000-2-222-2-222000000000000000000
χ17222222-2-222-2-2-2-2-2-22-2-2-2-22222000000000000000022-2-222-2-20000000000
χ18222222-2-222-2-2-2-2-2-22-2-2-2-222220000000000000000-2-222-2-2220000000000
χ19222222-2-2-2-2-2-20000-222000000000022-2-222−2−2−2−22222−2−2−2−2220000000000
χ20222222-2-2-2-2-2-20000-222000000000022-2-2−2−22222−2−2−2−22222−2−20000000000
χ21222222-2-2-2-2-2-20000-2220000000000-2-22222−2−2−2−222−2−22222−2−20000000000
χ22222222-2-2-2-2-2-20000-2220000000000-2-222−2−22222−2−222−2−2−2−2220000000000
χ232222-2-22222-2-22222-22-2-2-2-2-222000000000000000000000000000002-2000
χ242222-2-22222-2-22222-22-2-2-2-2-22200000000000000000000000000000-22000
χ252222-2-22222-2-2-2-2-2-2-22-22222-2-20000000000000000000000002i2i−2i−2i000000
χ262222-2-22222-2-2-2-2-2-2-22-22222-2-2000000000000000000000000−2i−2i2i2i000000
χ272222-2-2-2-222222222-2-22-2-222-2-2000000000000000000000000000020000-2
χ282222-2-2-2-222222222-2-22-2-222-2-20000000000000000000000000000-200002
χ292222-2-2-2-22222-2-2-2-2-2-2222-2-22200000000000000000000000000000002-20
χ302222-2-2-2-22222-2-2-2-2-2-2222-2-2220000000000000000000000000000000-220
χ312-2-222-22-2002-22−22−20002−22−22−2002-22−22−2ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ70000000000
χ322-2-222-22-2002-22−22−20002−22−22−2002-22−22−2−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ70000000000
χ332-2-222-22-2002-22−22−20002−22−22−200-22−22−22ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ70000000000
χ342-2-222-22-2002-22−22−20002−22−22−200-22−22−22−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ70000000000
χ352-2-222-22-2002-2−22−22000−22−22−22002-2−22−22ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ50000000000
χ362-2-222-22-2002-2−22−22000−22−22−22002-2−22−22−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ50000000000
χ372-2-222-22-2002-2−22−22000−22−22−2200-222−22−2ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ50000000000
χ382-2-222-22-2002-2−22−22000−22−22−2200-222−22−2−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ50000000000
χ392-2-222-2-2200-222−22−20002−2−22−222-2002−2−22ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ50000000000
χ402-2-222-2-2200-222−22−20002−2−22−222-2002−2−22−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ50000000000
χ412-2-222-2-2200-222−22−20002−2−22−22-2200−222−2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ50000000000
χ422-2-222-2-2200-222−22−20002−2−22−22-2200−222−2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ50000000000
χ432-2-222-2-2200-22−22−22000−222−22−22-200−222−2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ70000000000
χ442-2-222-2-2200-22−22−22000−222−22−22-200−222−2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ70000000000
χ452-2-222-2-2200-22−22−22000−222−22−2-22002−2−22ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ70000000000
χ462-2-222-2-2200-22−22−22000−222−22−2-22002−2−22−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ70000000000
χ474444-4-444-4-4-4-400004-440000000000000000000000000000000000000000
χ484444-4-4-4-4-4-444000044-40000000000000000000000000000000000000000
χ4944-4-400004-40044-4-40000000000000000000000000000000002-22-2000000
χ5044-4-400004-40044-4-4000000000000000000000000000000000-22-22000000
χ5144-4-400004-400-4-4440000000000000000000000000000000002i−2i−2i2i000000
χ5244-4-400004-400-4-444000000000000000000000000000000000−2i2i2i−2i000000
χ534-4-44-444-400-4422−2222−22000−2222−222222−220000000000000000000000000000000000
χ544-4-44-444-400-44−2222−222200022−2222−22−22220000000000000000000000000000000000
χ554-4-44-44-44004-422−2222−22000−222222−22−22220000000000000000000000000000000000
χ564-4-44-44-44004-4−2222−222200022−22−222222−220000000000000000000000000000000000
χ5788-8-80000-880000000000000000000000000000000000000000000000000
χ588-88-80000000042−42−42420000000000000000000000000000000000000000000
χ598-88-800000000−424242−420000000000000000000000000000000000000000000

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