Finite Group Databasebeta

← Group #489845

Character table — Group #489845

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222444444448888888888888888888888888161616161616161632323232
order122244444488882444888844444444816161616161616161616161616161616222244884488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1
χ91111-1-111111111-11-1-1-1-11111-1-111-1-1-11111-1-1-1-11111-1-1-1-11-111-1-11-11-11-1
χ101111-1-111111111-11-1-1-1-11111-1-111-1-1-1-1-1-1-11111-1-1-1-111111-111-1-11-1-11-11
χ111111-1-111111111-11-1-1-1-11111-1-1-1-111-11111-1-1-1-11111-1-1-1-1-11-1-1111-1-11-11
χ121111-1-111111111-11-1-1-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-11-1-1111-11-11-1
χ131111-1-111111111-11-1-1-1-111-1-11111-1-1-11111-1-1-1-1-1-1-1-111111-1-1-111-111-1-11
χ141111-1-111111111-11-1-1-1-111-1-11111-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111-11-111-1
χ151111-1-111111111-11-1-1-1-111-1-111-1-111-11111-1-1-1-1-1-1-1-11111-1111-1-1-11-111-1
χ161111-1-111111111-11-1-1-1-111-1-111-1-111-1-1-1-1-111111111-1-1-1-1-1111-1-1-111-1-11
χ172222222222-2-2-2-22222-2-2-2-222220000-20000000000000000000000-2-20000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-20000-20000000000000000000000220000
χ192222222-2-222222-2-22-222-2-2000022-2-2-20000000000000000-220000000000
χ202222222-2-222222-2-22-222-2-20000-2-222-200000000000000002-20000000000
χ212222222-2-22-2-2-2-2-2-22-2-2-2220000000020000000000000000002-22-2000000
χ222222222-2-22-2-2-2-2-2-22-2-2-222000000002000000000000000000-22-22000000
χ23222222-222-200002-2-2-200002-22-20000022−2−222−2−222−2−222−2−2000000000000
χ24222222-222-200002-2-2-200002-22-200000−2−222−2−222−2−222−2−222000000000000
χ25222222-222-200002-2-2-20000-22-220000022−2−222−2−2−2−222−2−222000000000000
χ26222222-222-200002-2-2-20000-22-2200000−2−222−2−22222−2−222−2−2000000000000
χ272222-2-22222-2-2-2-2-22-2-222-2-222-2-2000020000000000000000000000-220000
χ282222-2-22222-2-2-2-2-22-2-222-2-2-2-2220000200000000000000000000002-20000
χ292222-2-22-2-2222222-2-22-2-2-2-20000222220000000000000000-2-20000000000
χ302222-2-22-2-2222222-2-22-2-2-2-20000-2-2-2-220000000000000000220000000000
χ312222-2-22-2-22-2-2-2-22-2-22222200000000-20000000000000000002-2-22000000
χ322222-2-22-2-22-2-2-2-22-2-22222200000000-2000000000000000000-222-2000000
χ332222-2-2-222-20000-2-22200002-2-220000022−2−2−2−22222−2−2−2−222000000000000
χ342222-2-2-222-20000-2-22200002-2-2200000−2−22222−2−2−2−22222−2−2000000000000
χ352222-2-2-222-20000-2-2220000-222-20000022−2−2−2−222−2−22222−2−2000000000000
χ362222-2-2-222-20000-2-2220000-222-200000−2−22222−2−222−2−2−2−222000000000000
χ37444444-4-4-4-40000-44-4400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-40000444-400000000000000000000000000000000000000000
χ3944-4-40004-402222−22−2200000022−2200000000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000
χ4044-4-40004-402222−22−2200000022−220000000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000
χ4144-4-40004-40−22−222222000000−222200000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000
χ4244-4-40004-40−22−222222000000−22220000000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000
χ4344-4-4000-4402222−22−22000000−22220000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000
χ4444-4-4000-4402222−22−22000000−2222000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000
χ4544-4-4000-440−22−22222200000022−220000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000
χ4644-4-4000-440−22−22222200000022−22000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000
χ474-44-44i−4i000022−2222−2200002i2−2i20000000000000000000ζ−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−ζ7000000000000
χ484-44-44i−4i000022−2222−2200002i2−2i20000000000000000000−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+ζ7000000000000
χ494-44-44i−4i0000−2222−22220000−2i22i20000000000000000000ζ+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−ζ7000000000000
χ504-44-44i−4i0000−2222−22220000−2i22i20000000000000000000−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+ζ7000000000000
χ514-44-4−4i4i000022−2222−220000−2i22i20000000000000000000ζ−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+ζ7000000000000
χ524-44-4−4i4i000022−2222−220000−2i22i20000000000000000000−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−ζ7000000000000
χ534-44-4−4i4i0000−2222−222200002i2−2i20000000000000000000ζ+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+ζ7000000000000
χ544-44-4−4i4i0000−2222−222200002i2−2i20000000000000000000−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−ζ7000000000000
χ554-4-4400400-44-4-440000000000004i−4i0000000000000000000000000000000
χ564-4-4400400-44-4-44000000000000−4i4i0000000000000000000000000000000
χ574-4-4400400-4-444-4000000000000004i−4i00000000000000000000000000000
χ584-4-4400400-4-444-400000000000000−4i4i00000000000000000000000000000
χ598-8-8800-80080000000000000000000000000000000000000000000000000

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