Finite Group Databasebeta

← Group #490114

Character table — Group #490114

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222224444444488888888888888888888816161616161616161616161616163232
order122222444488884444888824448161616161616161616161616161616162444444488888844
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ71111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ91111-1-1111111111-1-1-1-1-1111-1-11-11111-1-1-1-11111-1-1-1-11-11-111-1-11-111-1-11-1
χ101111-1-1111111111-1-1-1-1-1111-1-11-11111-1-1-1-11111-1-1-1-1-11-11-1-1111-1-1-111-11
χ111111-1-1111111111-1-1-1-1-1111-1-11-1-1-1-1-11111-1-1-1-111111-11-111-1-11-1-1-111-11
χ121111-1-1111111111-1-1-1-1-1111-1-11-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-111-1-11-1
χ131111-1-1111111111-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-111111-11-1-1-111-11-1-1111-1
χ141111-1-1111111111-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-11111-11-1111-1-1-1111-1-1-11
χ151111-1-1111111111-1-1-1-1-111-111-1-1-1-1-1-111111111-1-1-1-11-11-1-1-111-1111-1-1-11
χ161111-1-1111111111-1-1-1-1-111-111-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-1-11-1-1111-1
χ172222222222-2-2-2-22222-2-2-2-22222-2000000000000000000000000-2-2000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2-200000000000000000000000022000000
χ192222222-2-220000-2-22-2000022-2-2022−2−222−2−222−2−222−2−20000000000000000
χ202222222-2-220000-2-22-2000022-2-20−2−222−2−222−2−222−2−2220000000000000000
χ212222222-2-220000-2-22-20000-2-222022−2−222−2−2−2−222−2−2220000000000000000
χ222222222-2-220000-2-22-20000-2-2220−2−222−2−22222−2−222−2−20000000000000000
χ23222222-222-22222-2-2-2222-2-20000-2000000000000000022-2-2000000000000
χ24222222-222-22222-2-2-2222-2-20000-20000000000000000-2-222000000000000
χ25222222-222-2-2-2-2-2-2-2-22-2-22200002000000000000000000002-22-200000000
χ26222222-222-2-2-2-2-2-2-2-22-2-2220000200000000000000000000-22-2200000000
χ272222-2-22222-2-2-2-22-2-2-222-2-22-2-222000000000000000000000000-22000000
χ282222-2-22222-2-2-2-22-2-2-222-2-2-222-220000000000000000000000002-2000000
χ292222-2-22-2-220000-22-2200002-22-2022−2−2−2−22222−2−2−2−2220000000000000000
χ302222-2-22-2-220000-22-2200002-22-20−2−22222−2−2−2−22222−2−20000000000000000
χ312222-2-22-2-220000-22-220000-22-22022−2−2−2−222−2−22222−2−20000000000000000
χ322222-2-22-2-220000-22-220000-22-220−2−22222−2−222−2−2−2−2220000000000000000
χ332222-2-2-222-22222-222-2-2-2-2-20000200000000000000002-2-22000000000000
χ342222-2-2-222-22222-222-2-2-2-2-2000020000000000000000-222-2000000000000
χ352222-2-2-222-2-2-2-2-2-222-222220000-2000000000000000000002-2-2200000000
χ362222-2-2-222-2-2-2-2-2-222-222220000-200000000000000000000-222-200000000
χ37444444-4-4-4-4000044-4-400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-400004-44400000000000000000000000000000000000000000
χ3944-4-44-4000022−2222−22000022−22000000000000000ζ+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+ζ70000000000000000
χ4044-4-44-4000022−2222−22000022−22000000000000000−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−ζ70000000000000000
χ4144-4-44-40000−2222−22220000−2222000000000000000ζ−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−ζ70000000000000000
χ4244-4-44-40000−2222−22220000−2222000000000000000−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+ζ70000000000000000
χ4344-4-4-44000022−2222−220000−2222000000000000000ζ+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−ζ70000000000000000
χ4444-4-4-44000022−2222−220000−2222000000000000000−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+ζ70000000000000000
χ4544-4-4-440000−2222−2222000022−22000000000000000ζ−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+ζ70000000000000000
χ4644-4-4-440000−2222−2222000022−22000000000000000−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−ζ70000000000000000
χ474-44-400400-422−22−222200000022−22000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ70000000000000000000000000000
χ484-44-400400-422−22−222200000022−2200000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ70000000000000000000000000000
χ494-44-400400-4−222222−22000000−2222000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000
χ504-44-400400-4−222222−22000000−222200000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000
χ514-44-400-400422−22−2222000000−22220000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000
χ524-44-400-400422−22−2222000000−2222000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000
χ534-44-400-4004−222222−2200000022−220000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000
χ544-44-400-4004−222222−2200000022−22000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000
χ554-4-440004-4044-4-40000000000000000000000000000000000000002i2−2i20000
χ564-4-440004-4044-4-4000000000000000000000000000000000000000−2i22i20000
χ574-4-440004-40-4-4440000000000000000000000000000000000000000022−2200
χ584-4-440004-40-4-44400000000000000000000000000000000000000000−222200
χ598-8-88000-8800000000000000000000000000000000000000000000000000

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