Finite Group Databasebeta

← Group #489704

Character table — Group #489704

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12222244448888444444448888222222888881616161616161616444444161616162488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-111-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ91111-1-1111111111-1-1-111-1-1-1-1111-111-1-1-111-1-11111-1-1-1-11-111-1-111-1-11-11-1
χ101111-1-1111111111-1-1-111-1-1-1-1111-111-1-1-111-1-1-1-1-1-111111-111-1-1-1-111-11-11
χ111111-1-1111111111-1-1-111-1-1-1-1111-1-1-111-111-1-11111-1-1-1-1-11-1-11111-1-1-11-11
χ121111-1-1111111111-1-1-111-1-1-1-1111-1-1-111-111-1-1-1-1-1-11111-11-1-111-1-1111-11-1
χ131111-1-1111111111-1-1-1-1-111-1-111-1111-1-1-1-1-1111111-1-1-1-11-1-1-111-1-111-111-1
χ141111-1-1111111111-1-1-1-1-111-1-111-1111-1-1-1-1-111-1-1-1-111111-1-1-11111-1-11-1-11
χ151111-1-1111111111-1-1-1-1-111-1-111-11-1-111-1-1-1111111-1-1-1-1-1111-1-1-1-1111-1-11
χ161111-1-1111111111-1-1-1-1-111-1-111-11-1-111-1-1-111-1-1-1-11111-1111-1-111-1-1-111-1
χ172222222222-2-2-2-222222222-2-2-2-2220000-2-2-2-2-20000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000-222220000000000000000000000
χ192222222-2-222222-2-2-22000022-2-2002222-2000000000000-2-2000000000000
χ202222222-2-222222-2-2-22000022-2-200-2-2-2-2-200000000000022000000000000
χ212222222-2-22-2-2-2-2-2-2-220000-2-2220000002000000000000002-22-200000000
χ222222222-2-22-2-2-2-2-2-2-220000-2-222000000200000000000000-22-2200000000
χ23222222-222-20000-22-2-222220000-2-200000000022−2−222−2−20000002−22−20000
χ24222222-222-20000-22-2-222220000-2-2000000000−2−222−2−222000000−22−220000
χ25222222-222-20000-22-2-2-2-2-2-200002200000000022−2−222−2−2000000−22−220000
χ26222222-222-20000-22-2-2-2-2-2-2000022000000000−2−222−2−2220000002−22−20000
χ272222-2-22222-2-2-2-22-2-2-222-2-222-2-22-200002-2-2220000000000000000000000
χ282222-2-22222-2-2-2-22-2-2-2-2-22222-2-2-220000222-2-20000000000000000000000
χ292222-2-22-2-222222-222-20000-2-2-2-20022-2-22000000000000-22000000000000
χ302222-2-22-2-222222-222-20000-2-2-2-200-2-22220000000000002-2000000000000
χ312222-2-22-2-22-2-2-2-2-222-200002222000000-2000000000000002-2-2200000000
χ322222-2-22-2-22-2-2-2-2-222-200002222000000-200000000000000-222-200000000
χ332222-2-2-222-20000-2-22222-2-20000-2200000000022−2−2−2−2220000002−2−220000
χ342222-2-2-222-20000-2-22222-2-20000-22000000000−2−22222−2−2000000−222−20000
χ352222-2-2-222-20000-2-222-2-22200002-200000000022−2−2−2−222000000−222−20000
χ362222-2-2-222-20000-2-222-2-22200002-2000000000−2−22222−2−20000002−2−220000
χ37444444-4-4-4-400004-44-400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-4000044-4400000000000000000000000000000000000000000
χ3944-4-40004-402222−22−220000004i−4i0022−220000000002i2−2i20000000000000000000000
χ4044-4-40004-402222−22−22000000−4i4i0022−22000000000−2i22i20000000000000000000000
χ4144-4-40004-40−22−2222220000004i−4i00−2222000000000−2i22i20000000000000000000000
χ4244-4-40004-40−22−222222000000−4i4i00−22220000000002i2−2i20000000000000000000000
χ4344-4-4000-4402222−22−2200004i−4i0000−222200000002i2−2i2000000000000000000000000
χ4444-4-4000-4402222−22−220000−4i4i0000−22220000000−2i22i2000000000000000000000000
χ4544-4-4000-440−22−22222200004i−4i000022−220000000−2i22i2000000000000000000000000
χ4644-4-4000-440−22−2222220000−4i4i000022−2200000002i2−2i2000000000000000000000000
χ474-44-44-4000022−2222−220000000022−220000000000000ζ+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
χ484-44-44-4000022−2222−220000000022−220000000000000−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
χ494-44-44-40000−2222−222200000000−22220000000000000ζ−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
χ504-44-44-40000−2222−222200000000−22220000000000000−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
χ514-44-4-44000022−2222−2200000000−22220000000000000ζ+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
χ524-44-4-44000022−2222−2200000000−22220000000000000−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
χ534-44-4-440000−2222−22220000000022−220000000000000ζ−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
χ544-44-4-440000−2222−22220000000022−220000000000000−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
χ554-4-4400-40044-4-44000000000000004-400000000000000000000000000000
χ564-4-4400-40044-4-4400000000000000-4400000000000000000000000000000
χ574-4-4400-4004-444-400000000000000004-4000000000000000000000000000
χ584-4-4400-4004-444-40000000000000000-44000000000000000000000000000
χ598-8-8800800-80000000000000000000000000000000000000000000000000

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