Finite Group Databasebeta

← Group #489495

Character table — Group #489495

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444888888888888888888881616161616161616161632323232
order122244444424448888888824441616161616161616161616161616161622444444884488
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
χ51111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-1
χ91111-1-1-1-111-11-11-1-1-1-111111-11-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-11-1
χ101111-1-1-1-111-11-11-1-1-1-111111-11-11111-1-1-1-11111-1-1-1-1-11-11-11-111-1-11-11
χ111111-1-1-1-111-11-11-1-1-1-111111-11-1-1-1-1-11111-1-1-1-111111-11-11-11-11-1-11-11
χ121111-1-1-1-111-11-11-1-1-1-111111-11-1-1-1-1-11111-1-1-1-11111-11-11-11-111-11-11-1
χ131111-1-1-1-111-11-11-1-1-1-11111-11-111111-1-1-1-1-1-1-1-111111-1-111-1-11-111-1-11
χ141111-1-1-1-111-11-11-1-1-1-11111-11-111111-1-1-1-1-1-1-1-11111-111-1-111-1-11-111-1
χ151111-1-1-1-111-11-11-1-1-1-11111-11-11-1-1-1-111111111-1-1-1-11-1-111-1-11-11-111-1
χ161111-1-1-1-111-11-11-1-1-1-11111-11-11-1-1-1-111111111-1-1-1-1-111-1-111-1-111-1-11
χ1722222222222222-2-2-2-2-2-2-2-22222000000000000000000000000-2-20000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000220000
χ192222222222-2-2-2-222-2-222-2-2000000000000000000002200-2-200000000
χ202222222222-2-2-2-222-2-222-2-200000000000000000000-2-2002200000000
χ212222222222-2-2-2-2-2-222-2-22200000000000000000000002200-2-2000000
χ222222222222-2-2-2-2-2-222-2-2220000000000000000000000-2-20022000000
χ23222222-2-2-2-22-2-220000000022-2-222−2−222−2−222−2−222−2−200000000000000
χ24222222-2-2-2-22-2-220000000022-2-2−2−222−2−222−2−222−2−22200000000000000
χ25222222-2-2-2-22-2-2200000000-2-22222−2−222−2−2−2−222−2−22200000000000000
χ26222222-2-2-2-22-2-2200000000-2-222−2−222−2−22222−2−222−2−200000000000000
χ272222-2-222-2-2-2-222000000002-2-2222−2−2−2−22222−2−2−2−22200000000000000
χ282222-2-222-2-2-2-222000000002-2-22−2−22222−2−2−2−22222−2−200000000000000
χ292222-2-222-2-2-2-22200000000-222-222−2−2−2−222−2−22222−2−200000000000000
χ302222-2-222-2-2-2-22200000000-222-2−2−22222−2−222−2−2−2−22200000000000000
χ312222-2-2-2-2222-22-222-2-2-2-22200000000000000000000002-200-22000000
χ322222-2-2-2-2222-22-222-2-2-2-2220000000000000000000000-22002-2000000
χ332222-2-2-2-2222-22-2-2-22222-2-2000000000000000000002-200-2200000000
χ342222-2-2-2-2222-22-2-2-22222-2-200000000000000000000-22002-200000000
χ352222-2-2-2-222-22-222222-2-2-2-22-22-2000000000000000000000000-220000
χ362222-2-2-2-222-22-222222-2-2-2-2-22-220000000000000000000000002-20000
χ37444444-4-4-4-4-444-4000000000000000000000000000000000000000000
χ384444-4-444-4-444-4-4000000000000000000000000000000000000000000
χ394-44-400004-4000000004-40000000000000000002i2−2i22i2−2i200000000000000
χ404-44-400004-4000000004-4000000000000000000−2i22i2−2i22i200000000000000
χ414-44-400004-400000000-44000000000000002i2−2i22i2−2i2000000000000000000
χ424-44-400004-400000000-4400000000000000−2i22i2−2i22i2000000000000000000
χ434-44-40000-4400004-40000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ444-44-40000-4400004-4000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ454-44-40000-440000-440000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ464-44-40000-440000-44000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ474-4-44004-40000000022−220022−220000ζ+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
χ484-4-44004-40000000022−220022−220000−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
χ494-4-44004-400000000−222200−22220000ζ−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
χ504-4-44004-400000000−222200−22220000−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
χ514-4-4400-440000000022−2200−22220000ζ−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
χ524-4-4400-440000000022−2200−22220000−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
χ534-4-4400-4400000000−22220022−220000ζ+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
χ544-4-4400-4400000000−22220022−220000−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
χ5588-8-88-800000000000000000000000000000000000000000000000000
χ5688-8-8-8800000000000000000000000000000000000000000000000000

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