Finite Group Databasebeta

← Group #489481

Character table — Group #489481

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222224444444448888888888888888888881616161616161616161632323232
order122244448888244448888244481616161616161616161616161616161624444444882488
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
χ5111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1
χ6111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1
χ91111-1-111-1-1-1-1-11-1-11111111-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-11-1
χ101111-1-111-1-1-1-1-11-1-11111111-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-11-11
χ111111-1-111-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11-1-11-11
χ121111-1-111-1-1-1-1-11-1-11111111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-11-11-1
χ131111-1-111-1-1-1-1-11-1-111111-1-111-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111-1-11
χ141111-1-111-1-1-1-1-11-1-111111-1-111-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-111-1
χ151111-1-111-1-1-1-1-11-1-111111-1-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11-111-1
χ161111-1-111-1-1-1-1-11-1-111111-1-111-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-1-11
χ172222222222222-2-2-2-222-2-20000-2000000000000000000002-22-2000000
χ182222222222222-2-2-2-222-2-20000-200000000000000000000-22-22000000
χ1922222222-2-2-2-222222-2-2-2-22222-2000000000000000000000000-2-20000
χ2022222222-2-2-2-222222-2-2-2-2-2-2-2-2-2000000000000000000000000220000
χ2122222222-2-2-2-22-2-2-2-2-2-2220000200000000000000002-22-20000000000
χ2222222222-2-2-2-22-2-2-2-2-2-222000020000000000000000-22-220000000000
χ23222222-2-20000-2-22-2200002-22-2022−2−222−2−222−2−222−2−200000000000000
χ24222222-2-20000-2-22-2200002-22-20−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-20000-2-22-220000-22-22022−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-20000-2-22-220000-22-220−2−222−2−22222−2−222−2−200000000000000
χ272222-2-2222222-22-2-22-2-2-2-222-2-22000000000000000000000000-220000
χ282222-2-2222222-22-2-22-2-2-2-2-2-22220000000000000000000000002-20000
χ292222-2-2222222-2-222-2-2-2220000-200000000000000002-2-220000000000
χ302222-2-2222222-2-222-2-2-2220000-20000000000000000-222-20000000000
χ312222-2-222-2-2-2-2-2-222-222-2-200002000000000000000000002-2-22000000
χ322222-2-222-2-2-2-2-2-222-222-2-20000200000000000000000000-222-2000000
χ332222-2-2-2-200002-2-22200002-2-22022−2−2−2−22222−2−2−2−22200000000000000
χ342222-2-2-2-200002-2-22200002-2-220−2−22222−2−2−2−22222−2−200000000000000
χ352222-2-2-2-200002-2-2220000-222-2022−2−2−2−222−2−22222−2−200000000000000
χ362222-2-2-2-200002-2-2220000-222-20−2−22222−2−222−2−2−2−22200000000000000
χ37444444-4-40000-44-44-4000000000000000000000000000000000000000
χ384444-4-4-4-40000444-4-4000000000000000000000000000000000000000
χ3944-4-4004-4000000000004-4000000000000000002i2−2i22i2−2i200000000000000
χ4044-4-4004-4000000000004-400000000000000000−2i22i2−2i22i200000000000000
χ4144-4-4004-400000000000-4400000000000002i2−2i22i2−2i2000000000000000000
χ4244-4-4004-400000000000-440000000000000−2i22i2−2i22i2000000000000000000
χ4344-4-400-4444-4-400000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ4444-4-400-4444-4-40000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ4544-4-400-44-4-44400000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ4644-4-400-44-4-4440000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ474-44-44i−4i002i2−2i22i2−2i20000022−220000000ζ+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−ζ70000000000000000000000
χ484-44-44i−4i002i2−2i22i2−2i20000022−220000000−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+ζ70000000000000000000000
χ494-44-44i−4i00−2i22i2−2i22i200000−22220000000ζ−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−ζ70000000000000000000000
χ504-44-44i−4i00−2i22i2−2i22i200000−22220000000−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+ζ70000000000000000000000
χ514-44-4−4i4i002i2−2i22i2−2i200000−22220000000ζ−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+ζ70000000000000000000000
χ524-44-4−4i4i002i2−2i22i2−2i200000−22220000000−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−ζ70000000000000000000000
χ534-44-4−4i4i00−2i22i2−2i22i20000022−220000000ζ+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+ζ70000000000000000000000
χ544-44-4−4i4i00−2i22i2−2i22i20000022−220000000−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−ζ70000000000000000000000
χ558-8-8800004i2−4i2−4i24i200000000000000000000000000000000000000000000
χ568-8-880000−4i24i24i2−4i200000000000000000000000000000000000000000000

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