Finite Group Databasebeta

← Group #490155

Character table — Group #490155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222444444444444888888888888888161616161616161616161616161616163232
order12224444448888244444448888248888816161616161616164444444488881616161624
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111-1-111-1-11111-1-11-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111-1-111-1-11111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111111-1-111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ81111111111111111-1-111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-111111111-1-1111-1-1-1-1-1111-1-111-1-11111-1-1-1-11-11-111-1-111-1-111-1-11-1
χ101111-1-111111111-1-1111-1-1-1-1-1111-1-111-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-11
χ111111-1-111111111-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-111111-11-111-1-1-1-111-1-111-11
χ121111-1-111111111-1-1111-1-1-1-1-1111-1-111-1-1-1-1-1-11111-11-11-1-11111-1-1-1-1111-1
χ131111-1-111111111-1-1-1-11-111-1-111-11-1-1-1111111-1-1-1-11-11-1-1-11111-1-1-1-111-11
χ141111-1-111111111-1-1-1-11-111-1-111-11-1-1-1111111-1-1-1-1-11-1111-1-1-1-111-1-1111-1
χ151111-1-111111111-1-1-1-11-111-1-111-11-1-1-111-1-1-1-111111-11-1-1-111-1-11111-1-11-1
χ161111-1-111111111-1-1-1-11-111-1-111-11-1-1-111-1-1-1-11111-11-1111-1-111-1-111-1-1-11
χ172222222222-2-2-2-222222222-2-2-2-222-2-2-2-2-200000000000000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ1922222222-2-22222-2-200-220022-2-200-200000000000022-2-200000000000000
χ2022222222-2-22222-2-200-220022-2-200-2000000000000-2-22200000000000000
χ2122222222-2-2-2-2-2-2-2-200-2200-2-22200200000000000000002-22-20000000000
χ2222222222-2-2-2-2-2-2-2-200-2200-2-2220020000000000000000-22-220000000000
χ23222222-2-2220000-2222-2-2-2-20000-220000022−2−222−2−20000000000002−22−200
χ24222222-2-2220000-2222-2-2-2-20000-2200000−2−222−2−222000000000000−22−2200
χ25222222-2-2220000-22-2-2-2-22200002-20000022−2−222−2−2000000000000−22−2200
χ26222222-2-2220000-22-2-2-2-22200002-200000−2−222−2−2220000000000002−22−200
χ272222-2-22222-2-2-2-2-2-2222-2-2-222-2-22-22-2-22200000000000000000000000000
χ282222-2-22222-2-2-2-2-2-2-2-22-22222-2-2-22222-2-200000000000000000000000000
χ292222-2-222-2-222222200-2-200-2-2-2-20020000000000002-2-2200000000000000
χ302222-2-222-2-222222200-2-200-2-2-2-2002000000000000-222-200000000000000
χ312222-2-222-2-2-2-2-2-22200-2-200222200-200000000000000002-2-220000000000
χ322222-2-222-2-2-2-2-2-22200-2-200222200-20000000000000000-222-20000000000
χ332222-2-2-2-22200002-222-22220000-2-20000022−2−2−2−2220000000000002−2−2200
χ342222-2-2-2-22200002-222-22220000-2-200000−2−22222−2−2000000000000−222−200
χ352222-2-2-2-22200002-2-2-2-22-2-20000220000022−2−2−2−222000000000000−222−200
χ362222-2-2-2-22200002-2-2-2-22-2-200002200000−2−22222−2−20000000000002−2−2200
χ37444444-4-4-4-400004-4004-4000000000000000000000000000000000000000
χ384444-4-4-4-4-4-40000-440044000000000000000000000000000000000000000
χ3944-4-4004-40044-4-40000000000000000000000000000000000022−2200000000
χ4044-4-4004-40044-4-400000000000000000000000000000000000−222200000000
χ4144-4-4004-400-4-44400000000000000000000000000000000000002i2−2i2000000
χ4244-4-4004-400-4-4440000000000000000000000000000000000000−2i22i2000000
χ434-44-400004-422−2222−220000004i−4i0022−22000002i2−2i200000000000000000000000000
χ444-44-400004-422−2222−22000000−4i4i0022−2200000−2i22i200000000000000000000000000
χ454-44-400004-4−2222−22220000004i−4i00−222200000−2i22i200000000000000000000000000
χ464-44-400004-4−2222−2222000000−4i4i00−2222000002i2−2i200000000000000000000000000
χ474-44-40000-4422−2222−22004i−4i000000−22220002i2−2i20000000000000000000000000000
χ484-44-40000-4422−2222−2200−4i4i000000−2222000−2i22i20000000000000000000000000000
χ494-44-40000-44−2222−2222004i−4i00000022−22000−2i22i20000000000000000000000000000
χ504-44-40000-44−2222−222200−4i4i00000022−220002i2−2i20000000000000000000000000000
χ514-4-444-4000022−22−22220000000022−22000000000ζ−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−ζ7000000000000000000
χ524-4-444-4000022−22−22220000000022−22000000000−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+ζ7000000000000000000
χ534-4-444-40000−222222−2200000000−2222000000000ζ+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+ζ7000000000000000000
χ544-4-444-40000−222222−2200000000−2222000000000−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−ζ7000000000000000000
χ554-4-44-44000022−22−222200000000−2222000000000ζ−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+ζ7000000000000000000
χ564-4-44-44000022−22−222200000000−2222000000000−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−ζ7000000000000000000
χ574-4-44-440000−222222−220000000022−22000000000ζ+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−ζ7000000000000000000
χ584-4-44-440000−222222−220000000022−22000000000−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+ζ7000000000000000000
χ5988-8-800-88000000000000000000000000000000000000000000000000000

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