Finite Group Databasebeta

← Group #490849

Character table — Group #490849

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12222244448888444488888888224488888881616161616161616248888161616162444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ91111-1-111111111-1-1-1111-1-111-1-11111-11-111-1-11111-1-1-1-1-1-111-1-111-1-11-11-1
χ101111-1-111111111-1-1-1111-1-111-1-11111-11-111-1-1-1-1-1-11111-1-111-1-1-1-111-11-11
χ111111-1-111111111-1-1-1111-1-111-1-1-1-1-1-1-11-111-1-11111-1-1-1-111-1-11111-1-1-11-11
χ121111-1-111111111-1-1-1111-1-111-1-1-1-1-1-1-11-111-1-1-1-1-1-1111111-1-111-1-1111-11-1
χ131111-1-111111111-1-1-1111-1-1-1-1111111-1-11-1-1111111-1-1-1-1-1-1-1-111-1-111-111-1
χ141111-1-111111111-1-1-1111-1-1-1-1111111-1-11-1-111-1-1-1-11111-1-1-1-11111-1-11-1-11
χ151111-1-111111111-1-1-1111-1-1-1-111-1-1-1-1-1-11-1-1111111-1-1-1-11111-1-1-1-1111-1-11
χ161111-1-111111111-1-1-1111-1-1-1-111-1-1-1-1-1-11-1-111-1-1-1-111111111-1-111-1-1-111-1
χ172222222222-2-2-2-22222-2-2-2-222220000-222-2-2-2-20000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-20000-2-2-222220000000000000000000000
χ1922222222-2-222222-2-2-2-2-222000022-2-2-2000000000000002-2000000000000
χ2022222222-2-222222-2-2-2-2-2220000-2-222-200000000000000-22000000000000
χ2122222222-2-2-2-2-2-22-2-2-222-2-200000000200000000000000002i−2i2i−2i00000000
χ2222222222-2-2-2-2-2-22-2-2-222-2-20000000020000000000000000−2i2i−2i2i00000000
χ23222222-2-2220000-2-22-20000222200000-2-2000022−2−222−2−20000002−22−20000
χ24222222-2-2220000-2-22-20000222200000-2-20000−2−222−2−222000000−22−220000
χ25222222-2-2220000-2-22-20000-2-2-2-20000022000022−2−222−2−2000000−22−220000
χ26222222-2-2220000-2-22-20000-2-2-2-200000220000−2−222−2−2220000002−22−20000
χ272222-2-22222-2-2-2-2-2-2-22-2-22222-2-2000022-2-2-2220000000000000000000000
χ282222-2-22222-2-2-2-2-2-2-22-2-222-2-22200002-2222-2-20000000000000000000000
χ292222-2-222-2-22222-222-2-2-2-2-2000022-2-2200000000000000-22000000000000
χ302222-2-222-2-22222-222-2-2-2-2-20000-2-2222000000000000002-2000000000000
χ312222-2-222-2-2-2-2-2-2-222-2222200000000-200000000000000002i−2i−2i2i00000000
χ322222-2-222-2-2-2-2-2-2-222-2222200000000-20000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-222000022-2-2000022-2-200000-22000022−2−2−2−2220000002−2−220000
χ342222-2-2-2-222000022-2-2000022-2-200000-220000−2−22222−2−2000000−222−20000
χ352222-2-2-2-222000022-2-20000-2-222000002-2000022−2−2−2−222000000−222−20000
χ362222-2-2-2-222000022-2-20000-2-222000002-20000−2−22222−2−20000002−2−220000
χ37444444-4-4-4-40000-44-4400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-400004-44400000000000000000000000000000000000000000
χ3944-4-4004-40044-4-40000000000004-40000000000000000000000000000000
χ4044-4-4004-40044-4-4000000000000-440000000000000000000000000000000
χ4144-4-4004-400-4-444000000000000004i−4i00000000000000000000000000000
χ4244-4-4004-400-4-44400000000000000−4i4i00000000000000000000000000000
χ434-44-44-4000022−2222−2200000022−222i2−2i22i2−2i200000002i−2i2i−2i0000000000000000000000
χ444-44-44-4000022−2222−2200000022−22−2i22i2−2i22i20000000−2i2i−2i2i0000000000000000000000
χ454-44-44-40000−2222−2222000000−22222i2−2i22i2−2i20000000−2i2i−2i2i0000000000000000000000
χ464-44-44-40000−2222−2222000000−2222−2i22i2−2i22i200000002i−2i2i−2i0000000000000000000000
χ474-44-4-44000022−2222−22000000−22222i2−2i2−2i22i200000002i−2i−2i2i0000000000000000000000
χ484-44-4-44000022−2222−22000000−2222−2i22i22i2−2i20000000−2i2i2i−2i0000000000000000000000
χ494-44-4-440000−2222−222200000022−222i2−2i2−2i22i20000000−2i2i2i−2i0000000000000000000000
χ504-44-4-440000−2222−222200000022−22−2i22i22i2−2i200000002i−2i−2i2i0000000000000000000000
χ514-4-4400004-422−22−2222000022−22000000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000
χ524-4-4400004-422−22−2222000022−2200000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000
χ534-4-4400004-4−222222−220000−2222000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000
χ544-4-4400004-4−222222−220000−222200000000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000
χ554-4-440000-4422−22−22220000−22220000000000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ700000000000000
χ564-4-440000-4422−22−22220000−2222000000000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ700000000000000
χ574-4-440000-44−222222−22000022−220000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000
χ584-4-440000-44−222222−22000022−22000000000000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000
χ5988-8-800-88000000000000000000000000000000000000000000000000000

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