Finite Group Databasebeta

← Group #508181

Character table — Group #508181

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222244444448888888888888888816161616161616161616161632323232
order12222244444488884448888244488888161616161616161622244444161616162488
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-11-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111
χ811111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1
χ91111111-1-11111111-1-1-11-1-111-11-1-111-1-11111-1-1-1-111-11-1-11-111-1-11-11-1
χ101111111-1-11111111-1-1-11-1-111-11-1-111-1-11111-1-1-1-1-1-11-111-1111-1-1-11-11
χ111111111-1-11111111-1-1-11-1-111-11-1-111-1-1-1-1-1-1111111-11-1-11-1-1-111-11-11
χ121111111-1-11111111-1-1-11-1-111-11-1-111-1-1-1-1-1-11111-1-11-111-11-1-1111-11-1
χ131111111-1-11111111-1-1-11-1-11-11-11-1-1-1111111-1-1-1-1111-1-1-1-11-1-1111-1-11
χ141111111-1-11111111-1-1-11-1-11-11-11-1-1-1111111-1-1-1-1-1-1-11111-1-1-111-111-1
χ151111111-1-11111111-1-1-11-1-11-11-11-1-1-111-1-1-1-11111111-1-1-1-1111-1-1-111-1
χ161111111-1-11111111-1-1-11-1-11-11-11-1-1-111-1-1-1-11111-1-1-11111-111-1-11-1-11
χ17222222222222-2-2-2-2222-2-2-2-22222-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222-2-2222-2-2-2-2-2-2-2-222-22-22-22-2-222000000000000000000000000
χ202222222-2-2222-2-2-2-2-2-2-2-222-2-22-22222-2-2000000000000000000000000
χ212222-2-2222-2-2200002-2-200002-2-220000022−2−222−2−2000000002−22−20000
χ222222-2-2222-2-2200002-2-200002-2-2200000−2−222−2−22200000000−22−220000
χ232222-2-2222-2-2200002-2-20000-222-20000022−2−222−2−200000000−22−220000
χ242222-2-2222-2-2200002-2-20000-222-200000−2−222−2−222000000002−22−20000
χ252222-2-22-2-2-2-220000-222000022-2-20000022−2−2−2−222000000002−2−220000
χ262222-2-22-2-2-2-220000-222000022-2-200000−2−22222−2−200000000−222−20000
χ272222-2-22-2-2-2-220000-2220000-2-2220000022−2−2−2−22200000000−222−20000
χ282222-2-22-2-2-2-220000-2220000-2-22200000−2−22222−2−2000000002−2−220000
χ292222-2-2-22222-22222-22-2-222-20000-2000000000000002-2002-200000000
χ302222-2-2-22222-22222-22-2-222-20000-200000000000000-2200-2200000000
χ312222-2-2-22222-2-2-2-2-2-22-22-2-22000020000000000002-2002-20000000000
χ322222-2-2-22222-2-2-2-2-2-22-22-2-2200002000000000000-2200-220000000000
χ332222-2-2-2-2-222-222222-22-2-2-2-200002000000000000002200-2-200000000
χ342222-2-2-2-2-222-222222-22-2-2-2-20000200000000000000-2-2002200000000
χ352222-2-2-2-2-222-2-2-2-2-22-2222220000-20000000000002-200-220000000000
χ362222-2-2-2-2-222-2-2-2-2-22-2222220000-2000000000000-22002-20000000000
χ37444444-444-4-4-40000-4-440000000000000000000000000000000000000
χ38444444-4-4-4-4-4-4000044-40000000000000000000000000000000000000
χ3944-4-40004i−4i00022−2222−2200002i2−2i20000000000ζ+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
χ4044-4-40004i−4i00022−2222−2200002i2−2i20000000000−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
χ4144-4-40004i−4i000−2222−22220000−2i22i20000000000ζ−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
χ4244-4-40004i−4i000−2222−22220000−2i22i20000000000−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
χ4344-4-4000−4i4i00022−2222−220000−2i22i20000000000ζ+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
χ4444-4-4000−4i4i00022−2222−220000−2i22i20000000000−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
χ4544-4-4000−4i4i000−2222−222200002i2−2i20000000000ζ−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
χ4644-4-4000−4i4i000−2222−222200002i2−2i20000000000−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
χ474-44-44-44004-4-400000000000000004i−4i00000000000000000000000000
χ484-44-44-44004-4-40000000000000000−4i4i00000000000000000000000000
χ494-44-44-4-400-44444-4-4000-4004000000000000000000000000000000000
χ504-44-44-4-400-444-4-444000400-4000000000000000000000000000000000
χ514-44-4-44400-44-444-4-4000400-4000000000000000000000000000000000
χ524-44-4-44400-44-4-4-444000-4004000000000000000000000000000000000
χ534-44-4-44-4004-440000000000000000004-4000000000000000000000000
χ544-44-4-44-4004-44000000000000000000-44000000000000000000000000
χ558-8-880000000042−42−42420000000000000000000000000000000000000000
χ568-8-8800000000−424242−420000000000000000000000000000000000000000

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