Finite Group Databasebeta

← Group #490399

Character table — Group #490399

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222224444444488888888888888888888816161616161616161616161616163232
order122244444488882444888844448161616161616161616161616161616162224444488888844
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
χ51111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-11111-1-1
χ61111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-11111-1-1
χ911111-1-11111111-1-11-1-1-1111-11-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-111-111-1-11-1
χ1011111-1-11111111-1-11-1-1-1111-11-1-11111-1-1-1-11111-1-1-1-1-1-1-11111-11-1-1-111-11
χ1111111-1-11111111-1-11-1-1-1111-11-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-111-1-1-111-11
χ1211111-1-11111111-1-11-1-1-1111-11-1-1-1-1-1-11111-1-1-1-11111-1-1-11111-11-111-1-11-1
χ1311111-1-11111111-1-11-1-1-111-11-11-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1111-1-1-11
χ1411111-1-11111111-1-11-1-1-111-11-11-11111-1-1-1-1-1-1-1-11111-1-11-1-1111-11-1-1111-1
χ1511111-1-11111111-1-11-1-1-111-11-11-1-1-1-1-111111111-1-1-1-111-111-1-1-1-11-1-1111-1
χ1611111-1-11111111-1-11-1-1-111-11-11-1-1-1-1-111111111-1-1-1-1-1-11-1-1111-1111-1-1-11
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
χ192222222-2-2200002-2-2-200002-2-22022−2−222−2−222−2−222−2−20000000000000000
χ202222222-2-2200002-2-2-200002-2-220−2−222−2−222−2−222−2−2220000000000000000
χ212222222-2-2200002-2-2-20000-222-2022−2−222−2−2−2−222−2−2220000000000000000
χ222222222-2-2200002-2-2-20000-222-20−2−222−2−22222−2−222−2−20000000000000000
χ2322222-2-2222-2-2-2-2-2-22-222-2-22-22-22000000000000000000000000-22000000
χ2422222-2-2222-2-2-2-2-2-22-222-2-2-22-2220000000000000000000000002-2000000
χ2522222-2-2-2-220000-22-22000022-2-2022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222-2-2-2-220000-22-22000022-2-20−2−22222−2−2−2−22222−2−20000000000000000
χ2722222-2-2-2-220000-22-220000-2-222022−2−2−2−222−2−22222−2−20000000000000000
χ2822222-2-2-2-220000-22-220000-2-2220−2−22222−2−222−2−2−2−2220000000000000000
χ292222-22222-22222-2-2-2222-2-20000-200000000000000000022-200-200000000
χ302222-22222-22222-2-2-2222-2-20000-2000000000000000000-2-2200200000000
χ312222-22222-2-2-2-2-2-2-2-22-2-2220000200000000000000002-20002-2000000000
χ322222-22222-2-2-2-2-2-2-2-22-2-222000020000000000000000-22000-22000000000
χ332222-2-2-222-2222222-2-2-2-2-2-2000020000000000000000002-2200-200000000
χ342222-2-2-222-2222222-2-2-2-2-2-200002000000000000000000-22-200200000000
χ352222-2-2-222-2-2-2-2-222-2-222220000-200000000000000002-2000-22000000000
χ362222-2-2-222-2-2-2-2-222-2-222220000-20000000000000000-220002-2000000000
χ374444-444-4-4-40000-444-400000000000000000000000000000000000000000
χ384444-4-4-4-4-4-400004-44400000000000000000000000000000000000000000
χ3944-4-40004-4044-4-400000000000000000000000000000000000000022−220000
χ4044-4-40004-4044-4-4000000000000000000000000000000000000000−22220000
χ4144-4-40004-40-4-4440000000000000000000000000000000000000000022−2200
χ4244-4-40004-40-4-44400000000000000000000000000000000000000000−222200
χ434-44-404i−4i00022−2222−2200002i2−2i2000000000000000ζ+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
χ444-44-404i−4i00022−2222−2200002i2−2i2000000000000000−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
χ454-44-404i−4i000−2222−22220000−2i22i2000000000000000ζ−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
χ464-44-404i−4i000−2222−22220000−2i22i2000000000000000−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
χ474-44-40−4i4i00022−2222−220000−2i22i2000000000000000ζ+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
χ484-44-40−4i4i00022−2222−220000−2i22i2000000000000000−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
χ494-44-40−4i4i000−2222−222200002i2−2i2000000000000000ζ−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
χ504-44-40−4i4i000−2222−222200002i2−2i2000000000000000−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
χ514-4-4440000-422−22−222200000022−22000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000000000
χ524-4-4440000-422−22−222200000022−2200000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000000000
χ534-4-4440000-4−222222−22000000−2222000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000000000
χ544-4-4440000-4−222222−22000000−222200000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000000000
χ554-4-44-40000422−22−2222000000−22220000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ564-4-44-40000422−22−2222000000−2222000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ574-4-44-400004−222222−2200000022−220000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ584-4-44-400004−222222−2200000022−22000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ5988-8-8000-8800000000000000000000000000000000000000000000000000

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