Finite Group Databasebeta

← Group #489666

Character table — Group #489666

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222224444444448888888888888888888881616161616161616161632323232
order122244448888244448888444481616161616161616161616161616161624444444884488
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-111-111-1-111-1-1
χ9111111111111-11-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-111-111-1-1-11-11-11-1
χ10111111111111-11-1-1-1-1-11111-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-11111-1-11-11
χ11111111111111-11-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1111111-111-1-1-11-1-11-11
χ12111111111111-11-1-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1-11111-11-11-1
χ13111111111111-11-1-1-1-1-111-1-111-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111-1-11
χ14111111111111-11-1-1-1-1-111-1-111-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-111-1
χ15111111111111-11-1-1-1-1-111-1-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11-111-1
χ16111111111111-11-1-1-1-1-111-1-111-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-1-11
χ1722222222-2-2-2-222222-2-2-2-22222-2000000000000000000000000-2-20000
χ1822222222-2-2-2-222222-2-2-2-2-2-2-2-2-2000000000000000000000000220000
χ1922222222-2-2-2-2-22-2-2-222-2-222-2-22000000000000000000000000-220000
χ2022222222-2-2-2-2-22-2-2-222-2-2-2-22220000000000000000000000002-20000
χ2122222-2-2200002-22-2-200002-22-2022−2−222−2−222−2−222−2−200000000000000
χ2222222-2-2200002-22-2-200002-22-20−2−222−2−222−2−222−2−22200000000000000
χ2322222-2-2200002-22-2-20000-22-22022−2−222−2−2−2−222−2−22200000000000000
χ2422222-2-2200002-22-2-20000-22-220−2−222−2−22222−2−222−2−200000000000000
χ2522222-2-220000-2-2-22200002-2-22022−2−2−2−22222−2−2−2−22200000000000000
χ2622222-2-220000-2-2-22200002-2-220−2−22222−2−2−2−22222−2−200000000000000
χ2722222-2-220000-2-2-2220000-222-2022−2−2−2−222−2−22222−2−200000000000000
χ2822222-2-220000-2-2-2220000-222-20−2−22222−2−222−2−2−2−22200000000000000
χ292222-222-222222-2-2-2222-2-20000-200000000000000002-2200-200000000
χ302222-222-222222-2-2-2222-2-20000-20000000000000000-22-200200000000
χ312222-222-22222-2-222-2-2-2-2-20000200000000000000002-2-200200000000
χ322222-222-22222-2-222-2-2-2-2-2000020000000000000000-22200-200000000
χ332222-222-2-2-2-2-22-2-2-22-2-2220000200000000000000000002-202-2000000
χ342222-222-2-2-2-2-22-2-2-22-2-222000020000000000000000000-220-22000000
χ352222-222-2-2-2-2-2-2-222-222220000-200000000000000000002-20-22000000
χ362222-222-2-2-2-2-2-2-222-222220000-20000000000000000000-2202-2000000
χ374444-4-4-4-4000044-44-4000000000000000000000000000000000000000
χ384444-4-4-4-40000-444-44000000000000000000000000000000000000000
χ3944-4-4400-422−2222−22000000022−22000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ4044-4-4400-422−2222−22000000022−2200000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ4144-4-4400-4−2222−22220000000−2222000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ4244-4-4400-4−2222−22220000000−222200000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ4344-4-4-400422−2222−220000000−22220000000002ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ50000000000000000000000
χ4444-4-4-400422−2222−220000000−2222000000000−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ50000000000000000000000
χ4544-4-4-4004−2222−2222000000022−220000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ70000000000000000000000
χ4644-4-4-4004−2222−2222000000022−22000000000−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ70000000000000000000000
χ474-4-4404-4044-4-4000000000000000000000022−2222−22000000000000000000
χ484-4-4404-4044-4-40000000000000000000000−2222−2222000000000000000000
χ494-4-4404-40-4-444000000000000000000000000002i2−2i22i2−2i200000000000000
χ504-4-4404-40-4-44400000000000000000000000000−2i22i2−2i22i200000000000000
χ514-4-440-4400000000004i−4i0000000000000002-2-222i−2i−2i2i00000000000000
χ524-4-440-4400000000004i−4i000000000000000-222-2−2i2i2i−2i00000000000000
χ534-4-440-440000000000−4i4i0000000000000002-2-22−2i2i2i−2i00000000000000
χ544-4-440-440000000000−4i4i000000000000000-222-22i−2i−2i2i00000000000000
χ558-88-8000042−42−424200000000000000000000000000000000000000000000
χ568-88-80000−424242−4200000000000000000000000000000000000000000000

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