Finite Group Databasebeta

← Group #501237

Character table — Group #501237

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444888888888888888888888161616161616161616161616163232
order122222444488882244888816161616222444448881616161616161616161622444444888161628
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1
χ41111111111111111111111-1-1-1-11-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ51111111111111111111-1-111111-111-111-1-111-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ61111111111111111111-1-111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-111-1-111
χ71111111111111111111-1-11-1-1-1-1-111-111-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111
χ81111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1111111-11111-1-1
χ911111111111111-1-1-1-111111111-111-11111-1-1111-1-1-1-11111-1-111-1-1-1-1-111-1-1-11
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1111-1-1-1-1111111-1-11111-1-1-1-1-11-1
χ1111111111111111-1-1-1-11111-1-1-1-1-111-11111-1-11-1-11111-1-1-1-1-1-1-1-111-1-1-111111-1
χ1211111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-1-11111-1-1-1-11111-1-111-1-1-111-11
χ1311111111111111-1-1-1-11-1-111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1111-1
χ1411111111111111-1-1-1-11-1-1111111-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111111-11
χ1511111111111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-11
χ1611111111111111-1-1-1-11-1-11-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-11-1
χ172222222222-2-2-2-22222-222-20000200200-2-2-2-22000000000000000000-2000000
χ182222222222-2-2-2-22222-2-2-2-20000-200-20022-2-2-20000000000000000002000000
χ192222222222-2-2-2-2-2-2-2-2-222-20000-200-200-2-22220000000000000000002000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-200002002002222-2000000000000000000-2000000
χ212222-2-22-22-222220000-200-222220220-2-200000-2-20000000000-2200000000000
χ222222-2-22-22-222220000-200-222220-2-202200000-2-200000000002-200000000000
χ232222-2-22-22-222220000-200-2-2-2-2-20220-2-2000002200000000002-200000000000
χ242222-2-22-22-222220000-200-2-2-2-2-20-2-202200000220000000000-2200000000000
χ252222-2-2-22-22000022-2-2022022−2−2-2002000000-22−222−2−222−2−2000000000002−200
χ262222-2-2-22-22000022-2-20220−2−222-2002000000-2−22−2−222−2−22200000000000−2200
χ272222-2-2-22-22000022-2-20-2-2022−2−2200-200000022−222−2−2−2−22200000000000−2200
χ282222-2-2-22-22000022-2-20-2-20−2−222200-20000002−22−2−22222−2−2000000000002−200
χ292222-2-2-22-220000-2-222022022−2−2200-2000000-22−2−2−22222−2−200000000000−2200
χ302222-2-2-22-220000-2-2220220−2−222200-2000000-2−2222−2−2−2−222000000000002−200
χ312222-2-2-22-220000-2-2220-2-2022−2−2-200200000022−2−2−222−2−222000000000002−200
χ322222-2-2-22-220000-2-2220-2-20−2−222-20020000002−2222−2−222−2−200000000000−2200
χ332-2-222-2-222-222-2-20000200-2000002-202-200000002i−2i2i−2i000000002i−2i000000000
χ342-2-222-2-222-222-2-20000200-2000002-202-20000000−2i2i−2i2i00000000−2i2i000000000
χ352-2-222-2-222-222-2-20000200-200000-220-2200000002i−2i2i−2i00000000−2i2i000000000
χ362-2-222-2-222-222-2-20000200-200000-220-220000000−2i2i−2i2i000000002i−2i000000000
χ372-2-22-22-2-22222-2-22-22-2-2002000002-20-22002-2000000000002-20000000000000
χ382-2-22-22-2-22222-2-22-22-2-200200000-2202-2002-200000000000-220000000000000
χ392-2-22-22-2-22222-2-2-22-22-2002000002-20-2200-2200000000000-220000000000000
χ402-2-22-22-2-22222-2-2-22-22-200200000-2202-200-22000000000002-20000000000000
χ412-2-22-22-2-222-2-2222-22-2200-2000000000000-22000000000000000002-202-20000
χ422-2-22-22-2-222-2-2222-22-2200-2000000000000-2200000000000000000-220-220000
χ432-2-22-22-2-222-2-222-22-22200-20000000000002-2000000000000000002-20-220000
χ442-2-22-22-2-222-2-222-22-22200-20000000000002-200000000000000000-2202-20000
χ45444444-4-4-4-40000000000002222−22−2200000000000−222200000000000000000000000
χ46444444-4-4-4-4000000000000−22−2222220000000000022−2200000000000000000000000
χ474444-4-44-44-4-4-4-4-4000040040000000000000000000000000000000000000000
χ4844-4-400000022−2222−22000002i2−2i202ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000002i−2i000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000
χ4944-4-400000022−2222−22000002i2−2i20−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000002i−2i000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000
χ5044-4-400000022−2222−2200000−2i22i202ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000−2i2i000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000
χ5144-4-400000022−2222−2200000−2i22i20−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000−2i2i000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000
χ5244-4-4000000−2222−2222000002i2−2i202ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000−2i2i000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000
χ5344-4-4000000−2222−2222000002i2−2i20−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000−2i2i000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ5444-4-4000000−2222−222200000−2i22i202ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000002i−2i000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000
χ5544-4-4000000−2222−222200000−2i22i20−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000002i−2i000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000
χ564-4-444-44-4-4400004-4-4400000000000000000000000000000000000000000000
χ574-4-444-44-4-440000-444-400000000000000000000000000000000000000000000
χ584-4-444-4-444-4-4-4440000-40040000000000000000000000000000000000000000
χ594-4-44-4444-4-4000000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ604-4-44-4444-4-400000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ618-88-800000042−42−4242000000000000000000000000000000000000000000000000
χ628-88-8000000−424242−42000000000000000000000000000000000000000000000000

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