Finite Group Databasebeta

← Group #145728

Character table — Group #145728

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12222222224444888888884488881616161616161616161616161616161644448888161616161616161624444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ922222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000
χ112222222222-2-2-2-200000000-2-2000022222222−2−2−2−2−2−2−2−222-2-2000022−2−222−2−200000000
χ122222222222-2-2-2-200000000-2-2000022222222−2−2−2−2−2−2−2−2-2-2220000−2−222−2−22200000000
χ132222222222-2-2-2-200000000-2-20000−2−2−2−2−2−2−2−22222222222-2-20000−2−222−2−22200000000
χ142222222222-2-2-2-200000000-2-20000−2−2−2−2−2−2−2−222222222-2-222000022−2−222−2−200000000
χ1522222-2-2-22-22-2-222222-2-2-2-22-222-2-2000000000000000000000000000000000000002i−2i
χ1622222-2-2-22-22-2-222222-2-2-2-22-222-2-200000000000000000000000000000000000000−2i2i
χ1722222-2-2-22-22-2-22-2-2-2-222222-2-2-222000000000000000000000000000000002-2000000
χ1822222-2-2-22-22-2-22-2-2-2-222222-2-2-22200000000000000000000000000000000-22000000
χ192222-22-2-2-222-2-222222-2-2-2-2-22-2-2220000000000000000000000000000000000002i−2i00
χ202222-22-2-2-222-2-222222-2-2-2-2-22-2-222000000000000000000000000000000000000−2i2i00
χ212222-22-2-2-222-2-22-2-2-2-22222-2222-2-200000000000000000000000000000000002-20000
χ222222-22-2-2-222-2-22-2-2-2-22222-2222-2-20000000000000000000000000000000000-220000
χ232222-2-222-2-2222222222222-2-2-2-2-2-20000000000000000000000002222-2-2-2-200000000
χ242222-2-222-2-2222222222222-2-2-2-2-2-2000000000000000000000000-2-2-2-2222200000000
χ252222-2-222-2-22222-2-2-2-2-2-2-2-2-2-222222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ262222-2-222-2-22222-2-2-2-2-2-2-2-2-2-22222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ272222-2-222-2-2-2-2-2-200000000220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i2i−2i−2i22−2−2−2−22200000000
χ282222-2-222-2-2-2-2-2-200000000220000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i−2i2i2i−2−22222−2−200000000
χ292222-2-222-2-2-2-2-2-200000000220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i2i−2i−2i−2−22222−2−200000000
χ302222-2-222-2-2-2-2-2-200000000220000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i−2i2i2i22−2−2−2−22200000000
χ3122-2-22-22-2-22000022−2−22−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5002-22−22−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ3222-2-22-22-2-22000022−2−22−22−2002−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ500-22−22−22−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ3322-2-22-22-2-22000022−2−22−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5002-22−22−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ3422-2-22-22-2-22000022−2−22−22−2002−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ500-22−22−22ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ3522-2-22-22-2-220000−2−222−22−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7002-2−22−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ3622-2-22-22-2-220000−2−222−22−2200−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ700-222−22−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ3722-2-22-22-2-220000−2−222−22−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7002-2−22−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ3822-2-22-22-2-220000−2−222−22−2200−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ700-222−22−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ3922-2-2-222-22-2000022−2−22−22−200−22−22ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ52i−2i00i2−i2−i2i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ4022-2-2-222-22-2000022−2−22−22−200−22−22ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−2i2i00−i2i2i2−i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ4122-2-2-222-22-2000022−2−22−22−200−22−22−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ52i−2i00i2−i2−i2i2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000
χ4222-2-2-222-22-2000022−2−22−22−200−22−22−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−2i2i00−i2i2i2−i2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000
χ4322-2-2-222-22-20000−2−222−22−22002−22−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ72i−2i00−i2i2i2−i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ4422-2-2-222-22-20000−2−222−22−22002−22−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−2i2i00i2−i2−i2i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ4522-2-2-222-22-20000−2−222−22−22002−22−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ72i−2i00−i2i2i2−i2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000
χ4622-2-2-222-22-20000−2−222−22−22002−22−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−2i2i00i2−i2−i2i2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000
χ4744444-4-4-44-4-444-400000000-4400000000000000000000000000000000000000000000
χ484444-44-4-4-44-444-4000000004-400000000000000000000000000000000000000000000
χ4944-4-444-44-4-400002222−22−22−2222−22220022−22−22220000000000000000000000000000000000000000
χ5044-4-444-44-4-40000−22−22222222−2222−2200−222222−220000000000000000000000000000000000000000
χ5144-4-4-4-4-444400002222−22−22−2222−222200−222222−220000000000000000000000000000000000000000
χ5244-4-4-4-4-44440000−22−22222222−2222−220022−22−22220000000000000000000000000000000000000000
χ534-44-400000004i−4i02i2−2i22i2−2i222−22−22220000002ζ3−2ζ32ζ3−2ζ32ζ5−2ζ52ζ5−2ζ52ζ7−2ζ72ζ7−2ζ72ζ−2ζ2ζ−2ζ000000000000000000000000
χ544-44-400000004i−4i02i2−2i22i2−2i222−22−2222000000−2ζ32ζ3−2ζ32ζ3−2ζ52ζ5−2ζ52ζ5−2ζ72ζ7−2ζ72ζ7−2ζ2ζ−2ζ2ζ000000000000000000000000
χ554-44-400000004i−4i0−2i22i2−2i22i2−222222−220000002ζ7−2ζ72ζ7−2ζ72ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ52ζ5−2ζ52ζ5000000000000000000000000
χ564-44-400000004i−4i0−2i22i2−2i22i2−222222−22000000−2ζ72ζ7−2ζ72ζ7−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ5−2ζ52ζ5−2ζ5000000000000000000000000
χ574-44-40000000−4i4i02i2−2i22i2−2i2−222222−220000002ζ−2ζ2ζ−2ζ2ζ7−2ζ72ζ7−2ζ7−2ζ52ζ5−2ζ52ζ5−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ584-44-40000000−4i4i02i2−2i22i2−2i2−222222−22000000−2ζ2ζ−2ζ2ζ−2ζ72ζ7−2ζ72ζ72ζ5−2ζ52ζ5−2ζ52ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ594-44-40000000−4i4i0−2i22i2−2i22i222−22−22220000002ζ5−2ζ52ζ5−2ζ52ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ7−2ζ72ζ7−2ζ7000000000000000000000000
χ604-44-40000000−4i4i0−2i22i2−2i22i222−22−2222000000−2ζ52ζ5−2ζ52ζ5−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ72ζ7−2ζ72ζ7000000000000000000000000
χ614-4-44000000400-44i−4i−4i4i00000000002ζ2−2ζ2−2ζ22ζ2−2ζ62ζ62ζ6−2ζ62ζ2−2ζ2−2ζ22ζ2−2ζ62ζ62ζ6−2ζ6000000000000000000000000
χ624-4-44000000400-44i−4i−4i4i0000000000−2ζ22ζ22ζ2−2ζ22ζ6−2ζ6−2ζ62ζ6−2ζ22ζ22ζ2−2ζ22ζ6−2ζ6−2ζ62ζ6000000000000000000000000
χ634-4-44000000400-4−4i4i4i−4i00000000002ζ6−2ζ6−2ζ62ζ6−2ζ22ζ22ζ2−2ζ22ζ6−2ζ6−2ζ62ζ6−2ζ22ζ22ζ2−2ζ2000000000000000000000000
χ644-4-44000000400-4−4i4i4i−4i0000000000−2ζ62ζ62ζ6−2ζ62ζ2−2ζ2−2ζ22ζ2−2ζ62ζ62ζ6−2ζ62ζ2−2ζ2−2ζ22ζ2000000000000000000000000
χ654-4-44000000-4004000044-4-40000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ664-4-44000000-4004000044-4-4000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ674-4-44000000-40040000-4-4440000002-2-222-2-22-222-2-222-2000000000000000000000000
χ684-4-44000000-40040000-4-444000000-222-2-222-22-2-222-2-22000000000000000000000000

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