Finite Group Databasebeta

← Group #511675

Character table — Group #511675

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244444444444444444444444488888888888888883232323232323232
order122222224444888888884444444444448888888888881616161616161616161616161616161622444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ911111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ1011111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11
χ1111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11
χ1211111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-1
χ1311111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1
χ1511111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-111-1
χ1611111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-11-1-11
χ17222222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-22222000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-2000000000000000000000000
χ2122222222-2-2-2-20000000022-2-22222-2-2-2-200000000000022−2−222−2−222−2−222−2−200000000
χ2222222222-2-2-2-20000000022-2-22222-2-2-2-2000000000000−2−222−2−222−2−222−2−22200000000
χ2322222222-2-2-2-20000000022-2-2-2-2-2-2222200000000000022−2−222−2−2−2−222−2−22200000000
χ2422222222-2-2-2-20000000022-2-2-2-2-2-22222000000000000−2−222−2−22222−2−222−2−200000000
χ2522222222-2-2-2-200000000-2-22222-2-2-2-22200000000000022−2−2−2−22222−2−2−2−22200000000
χ2622222222-2-2-2-200000000-2-22222-2-2-2-222000000000000−2−22222−2−2−2−22222−2−200000000
χ2722222222-2-2-2-200000000-2-222-2-22222-2-200000000000022−2−2−2−222−2−22222−2−200000000
χ2822222222-2-2-2-200000000-2-222-2-22222-2-2000000000000−2−22222−2−222−2−2−2−22200000000
χ29222-2-22-2-2000022−2−222−2−2002-2002-22-20022−2−222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000
χ30222-2-22-2-2000022−2−222−2−2002-2002-22-20022−2−222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000
χ31222-2-22-2-2000022−2−222−2−2002-200-22-220022−2−2−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000
χ32222-2-22-2-2000022−2−222−2−2002-200-22-220022−2−2−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000
χ33222-2-22-2-2000022−2−222−2−200-22002-2-2200−2−222−2−22222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000
χ34222-2-22-2-2000022−2−222−2−200-22002-2-2200−2−222−2−22222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000
χ35222-2-22-2-2000022−2−222−2−200-2200-222-200−2−22222−2−2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000
χ36222-2-22-2-2000022−2−222−2−200-2200-222-200−2−22222−2−2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000
χ37222-2-22-2-20000−2−222−2−222002-2002-22-200−2−222−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000
χ38222-2-22-2-20000−2−222−2−222002-2002-22-200−2−222−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000
χ39222-2-22-2-20000−2−222−2−222002-200-22-2200−2−22222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000
χ40222-2-22-2-20000−2−222−2−222002-200-22-2200−2−22222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000
χ41222-2-22-2-20000−2−222−2−22200-22002-2-220022−2−222−2−2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000
χ42222-2-22-2-20000−2−222−2−22200-22002-2-220022−2−222−2−2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000
χ43222-2-22-2-20000−2−222−2−22200-2200-222-20022−2−2−2−22222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000
χ44222-2-22-2-20000−2−222−2−22200-2200-222-20022−2−2−2−22222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000
χ4544-444-4-4-4000022−2222−2222−2222−2200004-4000000000022−2222−220000000000000000000000000000
χ4644-444-4-4-4000022−2222−2222−2222−220000-440000000000−2222−22220000000000000000000000000000
χ4744-444-4-4-40000−2222−2222−2222−222200004-40000000000−2222−22220000000000000000000000000000
χ4844-444-4-4-40000−2222−2222−2222−22220000-44000000000022−2222−220000000000000000000000000000
χ4944-4-4-4-44444-4-40000000000000000000000004-4-440000000000000000000000000000
χ5044-4-4-4-44444-4-4000000000000000000000000-444-40000000000000000000000000000
χ5144-4-4-4-444-4-4444-4-444-4-44000000000000000000000000000000000000000000000000
χ5244-4-4-4-444-4-444-444-4-444-4000000000000000000000000000000000000000000000000
χ534-444-4-44-400002222−22−22−22−2222224i−4i00000000002i2−2i22i2−2i200000000000000000000000000000000
χ544-444-4-44-400002222−22−22−22−222222−4i4i0000000000−2i22i2−2i22i200000000000000000000000000000000
χ554-444-4-44-40000−22−2222222222−22−224i−4i0000000000−2i22i2−2i22i200000000000000000000000000000000
χ564-444-4-44-40000−22−2222222222−22−22−4i4i00000000002i2−2i22i2−2i200000000000000000000000000000000
χ574-44-44-4-444-44-4000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ584-44-44-4-444-44-400000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ594-44-44-4-44-44-444444-4-4-4-4000000000000000000000000000000000000000000000000
χ604-44-44-4-44-44-44-4-4-4-44444000000000000000000000000000000000000000000000000
χ614-4-44-44-444-4-444-4-44-444-4000000000000000000000000000000000000000000000000
χ624-4-44-44-444-4-44-444-44-4-44000000000000000000000000000000000000000000000000
χ634-4-44-44-44-444-400000000000000000000000000004-44-4000000000000000000000000
χ644-4-44-44-44-444-40000000000000000000000000000-44-44000000000000000000000000
χ654-4-4-4444-4000022−2222−22−2222−222200000000004-40000000022−22−2222000000000000000000000000
χ664-4-4-4444-4000022−2222−22−2222−22220000000000-4400000000−222222−22000000000000000000000000
χ674-4-4-4444-40000−2222−222222−2222−2200000000004-400000000−222222−22000000000000000000000000
χ684-4-4-4444-40000−2222−222222−2222−220000000000-440000000022−22−2222000000000000000000000000

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