Finite Group Databasebeta

← Group #489705

Character table — Group #489705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12224444448888222444448888222444888881616161616161616224444161616162488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-11111111111111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1111-1-11111-111-1111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111
χ6111111111111111-1-1111-1-11111-111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ7111111111111111-1-1111-1-11111-1-1-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-111-1-1
χ8111111111111111-1-1111-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111
χ911111-1-11111111-1111-1-1-1-1-1-111-1111-1-1-111-1-11111-1-1-1-111-11-1-111-1-11-11-1
χ1011111-1-11111111-1111-1-1-1-1-1-111-1111-1-1-111-1-1-1-1-1-1111111-11-1-1-1-111-11-11
χ1111111-1-11111111-1111-1-1-1-1-1-111-1-1-1111-111-1-11111-1-1-1-1-1-11-11111-1-1-11-11
χ1211111-1-11111111-1111-1-1-1-1-1-111-1-1-1111-111-1-1-1-1-1-11111-1-11-111-1-1111-11-1
χ1311111-1-11111111-1-1-11-1-111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-111-111-1
χ1411111-1-11111111-1-1-11-1-111-1-111111-1-1-1-1-1-111-1-1-1-11111-1-1-111111-1-11-1-11
χ1511111-1-11111111-1-1-11-1-111-1-1111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-1-1111-1-11
χ1611111-1-11111111-1-1-11-1-111-1-1111-1-1-111-1-1-111-1-1-1-11111111-1-1-111-1-1-111-1
χ172222222222-2-2-2-222222222-2-2-2-2200200-2-2-2-2-20000000000000000000000
χ182222222222-2-2-2-22-2-2222-2-2-2-2-2-2-200-200-222220000000000000000000000
χ192222222-2-220000-222-22-2220000-200-2000000022−2−222−2−20000002−22−20000
χ202222222-2-220000-222-22-2220000-200-20000000−2−222−2−222000000−22−220000
χ212222222-2-220000-2-2-2-22-2-2-200002002000000022−2−222−2−2000000−22−220000
χ222222222-2-220000-2-2-2-22-2-2-2000020020000000−2−222−2−2220000002−22−20000
χ2322222-2-2222-2-2-2-2-2222-2-2-2-222-2-2-2002002-2-2220000000000000000000000
χ2422222-2-2222-2-2-2-2-2-2-22-2-22222-2-2200-200222-2-20000000000000000000000
χ2522222-2-2-2-220000222-2-22-2-20000200-2000000022−2−2−2−2220000002−2−220000
χ2622222-2-2-2-220000222-2-22-2-20000200-20000000−2−22222−2−2000000−222−20000
χ2722222-2-2-2-2200002-2-2-2-22220000-2002000000022−2−2−2−222000000−222−20000
χ2822222-2-2-2-2200002-2-2-2-22220000-20020000000−2−22222−2−20000002−2−220000
χ292222-22222-22222200-2-2-20022-2-2022022-200000000000000-2-20000000000
χ302222-22222-22222200-2-2-20022-2-20-2-20-2-2-200000000000000220000000000
χ312222-22222-2-2-2-2-2200-2-2-200-2-22200000020000000000002-2002-200000000
χ322222-22222-2-2-2-2-2200-2-2-200-2-2220000002000000000000-2200-2200000000
χ332222-2-2-222-22222-200-22200-2-2-2-20220-2-22000000000000002-20000000000
χ342222-2-2-222-22222-200-22200-2-2-2-20-2-2022200000000000000-220000000000
χ352222-2-2-222-2-2-2-2-2-200-222002222000000-20000000000002-200-2200000000
χ362222-2-2-222-2-2-2-2-2-200-222002222000000-2000000000000-22002-200000000
χ374444-444-4-4-40000-4004-44000000000000000000000000000000000000000
χ384444-4-4-4-4-4-4000040044-4000000000000000000000000000000000000000
χ3944-4-404i−4i0002222−22−22000000002i2−2i20000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000
χ4044-4-404i−4i0002222−22−22000000002i2−2i20000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000
χ4144-4-404i−4i000−22−22222200000000−2i22i20000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000
χ4244-4-404i−4i000−22−22222200000000−2i22i20000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000
χ4344-4-40−4i4i0002222−22−2200000000−2i22i20000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000
χ4444-4-40−4i4i0002222−22−2200000000−2i22i20000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000
χ4544-4-40−4i4i000−22−222222000000002i2−2i20000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000
χ4644-4-40−4i4i000−22−222222000000002i2−2i20000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000
χ474-44-440000-422−2222−220000004i−4i0022−220000000002i2−2i20000000000000000000000
χ484-44-440000-422−2222−22000000−4i4i0022−22000000000−2i22i20000000000000000000000
χ494-44-440000-4−2222−22220000004i−4i00−2222000000000−2i22i20000000000000000000000
χ504-44-440000-4−2222−2222000000−4i4i00−22220000000002i2−2i20000000000000000000000
χ514-44-4-40000422−2222−2204-40000000−2222000000022−22000000000000000000000000
χ524-44-4-40000422−2222−220-440000000−22220000000−2222000000000000000000000000
χ534-44-4-400004−2222−222204-4000000022−220000000−2222000000000000000000000000
χ544-44-4-400004−2222−22220-44000000022−22000000022−22000000000000000000000000
χ554-4-44000-4404-4-4400000000000000004-4000000000000000000000000000
χ564-4-44000-4404-4-440000000000000000-44000000000000000000000000000
χ574-4-44000-440-444-400000000000004-4000000000000000000000000000000
χ584-4-44000-440-444-40000000000000-44000000000000000000000000000000
χ598-8-880008-800000000000000000000000000000000000000000000000000

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