Finite Group Databasebeta

← Group #134853

Character table — Group #134853

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order12222244444444888888884488881616161616161616161616161616161644448888161616161616161688888888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911111111-111-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1i−ii−ii−ii−i
χ1011111111-111-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−ii−ii−ii−ii
χ1111111111-111-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111i−ii−i−ii−ii
χ1211111111-111-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111−ii−iii−ii−i
χ1311111111-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111i−i−iii−i−ii
χ1411111111-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111−iii−i−iii−i
χ1511111111-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1i−i−ii−iii−i
χ1611111111-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1−iii−ii−i−ii
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000
χ1922222222-222-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000022-2-2-2-2220000000000000000
χ2022222222-222-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-22222-2-20000000000000000
χ21222222-2-22-2-222200000000-2-200002222−2−2−2−22222−2−2−2−22-22-2000022−2−222−2−200000000
χ22222222-2-22-2-222200000000-2-200002222−2−2−2−22222−2−2−2−2-22-220000−2−222−2−22200000000
χ23222222-2-22-2-222200000000-2-20000−2−2−2−22222−2−2−2−222222-22-20000−2−222−2−22200000000
χ24222222-2-22-2-222200000000-2-20000−2−2−2−22222−2−2−2−22222-22-22000022−2−222−2−200000000
χ25222222-2-2-2-2-2-2-2-2000000002200002222−2−2−2−2−2−2−2−222222-2-22000022−2−2−2−22200000000
χ26222222-2-2-2-2-2-2-2-2000000002200002222−2−2−2−2−2−2−2−22222-222-20000−2−22222−2−200000000
χ27222222-2-2-2-2-2-2-2-200000000220000−2−2−2−222222222−2−2−2−22-2-220000−2−22222−2−200000000
χ28222222-2-2-2-2-2-2-2-200000000220000−2−2−2−222222222−2−2−2−2-222-2000022−2−2−2−22200000000
χ292222-2-2222-2-2-2-22000000002-2000022−2−222−2−222−2−222−2−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000000
χ302222-2-2222-2-2-2-22000000002-2000022−2−222−2−222−2−222−2−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000000
χ312222-2-2222-2-2-2-22000000002-20000−2−222−2−222−2−222−2−22200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i200000000
χ322222-2-2222-2-2-2-22000000002-20000−2−222−2−222−2−222−2−2220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i200000000
χ332222-2-222-2-2-222-200000000-22000022−2−222−2−2−2−222−2−22200002i−2i−2i2ii2−i2i2−i2−i2i2−i2i200000000
χ342222-2-222-2-2-222-200000000-22000022−2−222−2−2−2−222−2−2220000−2i2i2i−2i−i2i2−i2i2i2−i2i2−i200000000
χ352222-2-222-2-2-222-200000000-220000−2−222−2−22222−2−222−2−200002i−2i−2i2i−i2i2−i2i2i2−i2i2−i200000000
χ362222-2-222-2-2-222-200000000-220000−2−222−2−22222−2−222−2−20000−2i2i2i−2ii2−i2i2−i2−i2i2−i2i200000000
χ372222-2-2-2-2222-2-222222-2-2-2-2-2222-2-20000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ382222-2-2-2-2222-2-222222-2-2-2-2-2222-2-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ392222-2-2-2-2222-2-22-2-2-2-22222-22-2-22222-2-2-2-22222-2-2-2-222000000000000000000000000
χ402222-2-2-2-2222-2-22-2-2-2-22222-22-2-222-2-22222-2-2-2-22222-2-2000000000000000000000000
χ412222-2-2-2-2-22222-22222-2-2-2-22-2-2-2220000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ422222-2-2-2-2-22222-22222-2-2-2-22-2-2-222000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ432222-2-2-2-2-22222-2-2-2-2-222222-222-2-222-2-2-2-222-2-22222-2-2000000000000000000000000
χ442222-2-2-2-2-22222-2-2-2-2-222222-222-2-2-2-22222-2-222-2-2-2-222000000000000000000000000
χ4544-4-4000004-4000000044-4-4000000004-44-40000000000000000000000000000000000
χ4644-4-4000004-4000000044-4-400000000-44-440000000000000000000000000000000000
χ4744-4-4000004-40000000-4-4440000004i−4i00004i−4i00000000000000000000000000000000
χ4844-4-4000004-40000000-4-444000000−4i4i0000−4i4i00000000000000000000000000000000
χ4944-4-400000-440004i4i−4i−4i00000000002i2−2i222−22−2222−2i22i200000000000000000000000000000000
χ5044-4-400000-440004i4i−4i−4i0000000000−2i22i2−222222−222i2−2i200000000000000000000000000000000
χ5144-4-400000-44000−4i−4i4i4i00000000002i2−2i2−222222−22−2i22i200000000000000000000000000000000
χ5244-4-400000-44000−4i−4i4i4i0000000000−2i22i222−22−22222i2−2i200000000000000000000000000000000
χ534-44-4004i−4i0000002i2−2i22i2−2i222−2222−22000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ544-44-4004i−4i0000002i2−2i22i2−2i222−2222−2200000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ554-44-4004i−4i000000−2i22i2−2i22i2−2222−2222000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ564-44-4004i−4i000000−2i22i2−2i22i2−2222−222200000000000000−2ζ+2ζ72ζ−2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ574-44-400−4i4i0000002i2−2i22i2−2i2−2222−2222000000000000002ζ−2ζ7−2ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000
χ584-44-400−4i4i0000002i2−2i22i2−2i2−2222−222200000000000000−2ζ+2ζ72ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000
χ594-44-400−4i4i000000−2i22i2−2i22i222−2222−22000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ−2ζ7−2ζ+2ζ7000000000000000000000000
χ604-44-400−4i4i000000−2i22i2−2i22i222−2222−2200000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ+2ζ72ζ−2ζ7000000000000000000000000
χ614-4-444-4004004-4-422−22−222222−22−22220022−2222−220000000000000000000000000000000000000000
χ624-4-444-4004004-4-4−222222−22−222222−2200−2222−22220000000000000000000000000000000000000000
χ634-4-444-400-400-44422−22−222222−22−222200−2222−22220000000000000000000000000000000000000000
χ644-4-444-400-400-444−222222−22−222222−220022−2222−220000000000000000000000000000000000000000
χ654-4-44-4400400-44-422−22−2222−222222−220022−22−22220000000000000000000000000000000000000000
χ664-4-44-4400400-44-4−222222−2222−22−222200−222222−220000000000000000000000000000000000000000
χ674-4-44-4400-4004-4422−22−2222−222222−2200−222222−220000000000000000000000000000000000000000
χ684-4-44-4400-4004-44−222222−2222−22−22220022−22−22220000000000000000000000000000000000000000

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