Finite Group Databasebeta

← Group #504787

Character table — Group #504787

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222444444444444888888888888888888888161616161616161616161616163232
order122222444488884444888816161616444444448881616161616161616161622224444888161648
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-11-1-1111111111111111-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-1-1
χ41111111111111111111111-1-1-1-11-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-111
χ51111111111111111111-1-111111-111-111-1-111-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1
χ61111111111111111111-1-111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-111-1-1-111-1-111
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
χ911111111111111-1-1-1-111111111-111-11111-1-11-1-1-1-1111111-1-1-1-1-1-111-111-1-1-11
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-11-1
χ1111111111111111-1-1-1-11111-1-1-1-1-111-11111-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1
χ1211111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-111-1-11111-1-1-111-11
χ1311111111111111-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-1111-1
χ1411111111111111-1-1-1-11-1-1111111-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-11
χ1511111111111111-1-1-1-11-1-11-1-1-1-1111111-1-1-1-1-11111-1-11111-1-11111-1-11-1-1-1-1-11
χ1611111111111111-1-1-1-11-1-11-1-1-1-11-1-11-1-1-1-1-1-1-11111-1-1111111-1-1-1-111111-1-11-1
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
χ212222-2-222-2-222220000-200-222220220-2-2000000000-2-200000000002-20000000
χ222222-2-222-2-222220000-200-222220-2-2022000000000-2-20000000000-220000000
χ232222-2-222-2-222220000-200-2-2-2-2-20220-2-2000000000220000000000-220000000
χ242222-2-222-2-222220000-200-2-2-2-2-20-2-20220000000002200000000002-20000000
χ252222-2-2-2-222000022-2-2022022−2−2-2002000000-222−2−22−222−2−2000000000002−200
χ262222-2-2-2-222000022-2-20220−2−222-2002000000-2−2−222−22−2−22200000000000−2200
χ272222-2-2-2-222000022-2-20-2-2022−2−2200-2000000222−2−22−2−2−22200000000000−2200
χ282222-2-2-2-222000022-2-20-2-20−2−222200-20000002−2−222−2222−2−2000000000002−200
χ292222-2-2-2-2220000-2-222022022−2−2200-2000000-2−2−2222−222−2−200000000000−2200
χ302222-2-2-2-2220000-2-2220220−2−222200-2000000-222−2−2−22−2−222000000000002−200
χ312222-2-2-2-2220000-2-2220-2-2022−2−2-20020000002−2−2222−2−2−222000000000002−200
χ322222-2-2-2-2220000-2-2220-2-20−2−222-2002000000222−2−2−2222−2−200000000000−2200
χ3322-2-22-22-22-2-2-2220000-2002000002i−2i02i−2i000002i−2i2i−2i000000002-200000000000
χ3422-2-22-22-22-2-2-2220000-2002000002i−2i02i−2i00000−2i2i−2i2i00000000-2200000000000
χ3522-2-22-22-22-2-2-2220000-200200000−2i2i0−2i2i000002i−2i2i−2i00000000-2200000000000
χ3622-2-22-22-22-2-2-2220000-200200000−2i2i0−2i2i00000−2i2i−2i2i000000002-200000000000
χ3722-2-2-222-2-2222-2-22i−2i2i−2i-20020000000000002i−2i0000000000000002-20002i−2i0000
χ3822-2-2-222-2-2222-2-22i−2i2i−2i-20020000000000002i−2i000000000000000-22000−2i2i0000
χ3922-2-2-222-2-2222-2-2−2i2i−2i2i-2002000000000000−2i2i0000000000000002-2000−2i2i0000
χ4022-2-2-222-2-2222-2-2−2i2i−2i2i-2002000000000000−2i2i000000000000000-220002i−2i0000
χ4122-2-2-222-2-22-2-2222i−2i2i−2i200-2000002i−2i0−2i2i00−2i2i000000000002-20000000000000
χ4222-2-2-222-2-22-2-2222i−2i2i−2i200-200000−2i2i02i−2i00−2i2i00000000000-220000000000000
χ4322-2-2-222-2-22-2-222−2i2i−2i2i200-2000002i−2i0−2i2i002i−2i00000000000-220000000000000
χ4422-2-2-222-2-22-2-222−2i2i−2i2i200-200000−2i2i02i−2i002i−2i000000000002-20000000000000
χ45444444-4-4-4-40000000000002222−22−22000000000000000−22220000000000000000000
χ46444444-4-4-4-4000000000000−22−22222200000000000000022−220000000000000000000
χ474444-4-444-4-4-4-4-4-4000040040000000000000000000000000000000000000000
χ4844-4-44-44-44-444-4-40000400-40000000000000000000000000000000000000000
χ4944-4-44-4-44-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ5044-4-44-4-44-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5144-4-4-44-444-40000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5244-4-4-44-444-4000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ534-44-400000022−2222−22000002i2−2i202ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ50000002i−2i000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000
χ544-44-400000022−2222−22000002i2−2i20−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ50000002i−2i000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000
χ554-44-400000022−2222−2200000−2i22i202ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000−2i2i000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7000000000000000
χ564-44-400000022−2222−2200000−2i22i20−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000−2i2i000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7000000000000000
χ574-44-4000000−2222−2222000002i2−2i202ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000−2i2i000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000
χ584-44-4000000−2222−2222000002i2−2i20−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000−2i2i000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000
χ594-44-4000000−2222−222200000−2i22i202ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ70000002i−2i000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7000000000000000
χ604-44-4000000−2222−222200000−2i22i20−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ70000002i−2i000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7000000000000000
χ618-8-8800000042−42−4242000000000000000000000000000000000000000000000000
χ628-8-88000000−424242−42000000000000000000000000000000000000000000000000

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