Finite Group Databasebeta

← Group #489721

Character table — Group #489721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222444444448888888888888888888888888161616161616161632323232
order122244444488882444888822222244816161616161616161616161616161616224444882488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ51111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ91111-1-111111111-11-1-1-1-11111-1-11-11-1-11111-1-1-1-11111-1-1-1-111-1-11-11-11-11-1
χ101111-1-111111111-11-1-1-1-11111-1-11-11-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-11-11
χ111111-1-111111111-11-1-1-1-11111-1-1-11-11-11111-1-1-1-1-1-1-1-11111-1-1111-1-111-1-11
χ121111-1-111111111-11-1-1-1-11111-1-1-11-11-1-1-1-1-111111111-1-1-1-1-1-1111-1-11-111-1
χ131111-1-111111111-11-1-1-1-111-1-1111-11-1-11111-1-1-1-11111-1-1-1-1-1-111-111-1-11-11
χ141111-1-111111111-11-1-1-1-111-1-1111-11-1-1-1-1-1-11111-1-1-1-11111-1-111-111-11-11-1
χ151111-1-111111111-11-1-1-1-111-1-111-11-11-11111-1-1-1-1-1-1-1-1111111-1-1-11-11-111-1
χ161111-1-111111111-11-1-1-1-111-1-111-11-11-1-1-1-1-111111111-1-1-1-111-1-1-11-111-1-11
χ172222222222-2-2-2-22222-2-2-2-200002222-20000000000000000000000-2-20000
χ182222222222-2-2-2-22222-2-2-2-20000-2-2-2-2-20000000000000000000000220000
χ192222222-2-222222-2-22-222-2-222-2-20000-200000000000000000000-22000000
χ202222222-2-222222-2-22-222-2-2-2-2220000-2000000000000000000002-2000000
χ212222222-2-22-2-2-2-2-2-22-2-2-22200000000200000000000000002-22-200000000
χ222222222-2-22-2-2-2-2-2-22-2-2-2220000000020000000000000000-22-2200000000
χ23222222-222-200002-2-2-2000000002-2-22022−2−222−2−222−2−222−2−2000000000000
χ24222222-222-200002-2-2-2000000002-2-220−2−222−2−222−2−222−2−222000000000000
χ25222222-222-200002-2-2-200000000-222-2022−2−222−2−2−2−222−2−222000000000000
χ26222222-222-200002-2-2-200000000-222-20−2−222−2−22222−2−222−2−2000000000000
χ272222-2-22222-2-2-2-2-22-2-222-2-200002-22-220000000000000000000000-220000
χ282222-2-22222-2-2-2-2-22-2-222-2-20000-22-22200000000000000000000002-20000
χ292222-2-22-2-2222222-2-22-2-2-2-222220000200000000000000000000-2-2000000
χ302222-2-22-2-2222222-2-22-2-2-2-2-2-2-2-2000020000000000000000000022000000
χ312222-2-22-2-22-2-2-2-22-2-22222200000000-200000000000000002-2-2200000000
χ322222-2-22-2-22-2-2-2-22-2-22222200000000-20000000000000000-222-200000000
χ332222-2-2-222-20000-2-2220000000022-2-2022−2−2−2−22222−2−2−2−222000000000000
χ342222-2-2-222-20000-2-2220000000022-2-20−2−22222−2−2−2−22222−2−2000000000000
χ352222-2-2-222-20000-2-22200000000-2-222022−2−2−2−222−2−22222−2−2000000000000
χ362222-2-2-222-20000-2-22200000000-2-2220−2−22222−2−222−2−2−2−222000000000000
χ37444444-4-4-4-40000-44-4400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-40000444-400000000000000000000000000000000000000000
χ3944-4-44i−4i00002222−22−2200002i2−2i20000000000000000000ζ+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
χ4044-4-44i−4i00002222−22−2200002i2−2i20000000000000000000−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
χ4144-4-44i−4i0000−22−2222220000−2i22i20000000000000000000ζ−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
χ4244-4-44i−4i0000−22−2222220000−2i22i20000000000000000000−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
χ4344-4-4−4i4i00002222−22−220000−2i22i20000000000000000000ζ+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
χ4444-4-4−4i4i00002222−22−220000−2i22i20000000000000000000−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
χ4544-4-4−4i4i0000−22−22222200002i2−2i20000000000000000000ζ−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
χ4644-4-4−4i4i0000−22−22222200002i2−2i20000000000000000000−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
χ474-44-400-40044-44-400000000004-4000000000000000000000000000000000
χ484-44-400-40044-44-40000000000-44000000000000000000000000000000000
χ494-44-400-4004-44-44000000004-400000000000000000000000000000000000
χ504-44-400-4004-44-4400000000-4400000000000000000000000000000000000
χ514-4-440004-4022−22−222200000022−2200000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000
χ524-4-440004-4022−22−222200000022−220000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000
χ534-4-440004-40−222222−22000000−222200000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000
χ544-4-440004-40−222222−22000000−22220000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000
χ554-4-44000-44022−22−2222000000−22220000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ564-4-44000-44022−22−2222000000−2222000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ574-4-44000-440−222222−2200000022−220000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ584-4-44000-440−222222−2200000022−22000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ598-88-800800-80000000000000000000000000000000000000000000000000

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