Finite Group Databasebeta

← Group #490659

Character table — Group #490659

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order1222444444448888222444488888888161616161616161644888161616161616161616161616888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ511111111111111111-1-11-1-111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111-1-11-1-111111-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111-1-1-1-111111111-111-111111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111-1-1-1-111111111-111-111111-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ111111-1-1-1-111111111-111-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ121111-1-1-1-111111111-111-111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ131111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ141111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ151111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222222-2-2-2-22222222-2-2-2-2-2-2-2-20000000022-2-2-2000000000000000000000000
χ18222222222222-2-2-2-22-2-22-2-22-2-2-2-2222200000000-2-2-222000000000000000000000000
χ1922222222-222-22222-200-200-2-2-22200002222222200-200-2-2-2-200000000000000000000
χ2022222222-222-22222-200-200-2-2-2220000-2-2-2-2-2-2-2-200-200222200000000000000000000
χ2122222222-222-2-2-2-2-2-200-200-222-2-20000000000000020000002i2i−2i−2i2i2i−2i−2i000000000000
χ2222222222-222-2-2-2-2-2-200-200-222-2-2000000000000002000000−2i−2i2i2i−2i−2i2i2i000000000000
χ23222222-2-22-2-220000222-2-2-2-20000000022−2−222−2−22-20002−22−22−22−22−22−2000000000000
χ24222222-2-22-2-220000222-2-2-2-200000000−2−222−2−2222-2000−22−22−22−22−22−22000000000000
χ25222222-2-22-2-2200002-2-2-222-20000000022−2−222−2−2-220002−22−2−22−22−22−22000000000000
χ26222222-2-22-2-2200002-2-2-222-200000000−2−222−2−222-22000−22−222−22−22−22−2000000000000
χ27222222-2-2-2-2-2-20000-200200200002i2i−2i−2i22−2−222−2−20002i−2i−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ28222222-2-2-2-2-2-20000-200200200002i2i−2i−2i−2−222−2−2220002i−2i2−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ29222222-2-2-2-2-2-20000-20020020000−2i−2i2i2i22−2−222−2−2000−2i2i−22−22−i2i2i2−i2−i2i2i2−i2000000000000
χ30222222-2-2-2-2-2-20000-20020020000−2i−2i2i2i−2−222−2−222000−2i2i2−22−2i2−i2−i2i2i2−i2−i2i2000000000000
χ312222-2-2222-2-220000-2222-2-2-20000000022−2−2−2−222-220002−2−222−22−2−22−22000000000000
χ322222-2-2222-2-220000-2222-2-2-200000000−2−22222−2−2-22000−222−2−22−222−22−2000000000000
χ332222-2-2222-2-220000-2-2-2222-20000000022−2−2−2−2222-20002−2−22−22−222−22−2000000000000
χ342222-2-2222-2-220000-2-2-2222-200000000−2−22222−2−22-2000−222−22−22−2−22−22000000000000
χ352222-2-222-2-2-2-20000200-200200002i2i−2i−2i22−2−2−2−222000−2i2i−222−2i2−i2−i2i2−i2i2i2−i2000000000000
χ362222-2-222-2-2-2-20000200-200200002i2i−2i−2i−2−22222−2−2000−2i2i2−2−22−i2i2i2−i2i2−i2−i2i2000000000000
χ372222-2-222-2-2-2-20000200-20020000−2i−2i2i2i22−2−2−2−2220002i−2i−222−2−i2i2i2−i2i2−i2−i2i2000000000000
χ382222-2-222-2-2-2-20000200-20020000−2i−2i2i2i−2−22222−2−20002i−2i2−2−22i2−i2−i2i2−i2i2i2−i2000000000000
χ392222-2-2-2-22222-2-2-2-2-222-2222-2-222-2-2-2-200000000-2-2222000000000000000000000000
χ402222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22-2-222222200000000222-2-2000000000000000000000000
χ412222-2-2-2-2-222-22222200200-2-2-2-2-200002222-2-2-2-200200-2-22200000000000000000000
χ422222-2-2-2-2-222-22222200200-2-2-2-2-20000-2-2-2-222220020022-2-200000000000000000000
χ432222-2-2-2-2-222-2-2-2-2-2200200-2222200000000000000-20000002i2i−2i−2i−2i−2i2i2i000000000000
χ442222-2-2-2-2-222-2-2-2-2-2200200-2222200000000000000-2000000−2i−2i2i2i2i2i−2i−2i000000000000
χ452-22-22i−2i2i−2i02-2022-2-20000000002i−2i00002-22-22i−2i2i−2i000000000000000002−2i2−i22−2i2−i20000
χ462-22-22i−2i2i−2i02-2022-2-20000000002i−2i00002-22-22i−2i2i−2i00000000000000000−22−i2i2−22−i2i20000
χ472-22-22i−2i2i−2i02-2022-2-20000000002i−2i0000-22-22−2i2i−2i2i000000000000000002−2i2−i2−22−i2i20000
χ482-22-22i−2i2i−2i02-2022-2-20000000002i−2i0000-22-22−2i2i−2i2i00000000000000000−22−i2i22−2i2−i20000
χ492-22-2−2i2i−2i2i02-2022-2-2000000000−2i2i00002-22-2−2i2i−2i2i000000000000000002−2−i2i22−2−i2i20000
χ502-22-2−2i2i−2i2i02-2022-2-2000000000−2i2i00002-22-2−2i2i−2i2i00000000000000000−22i2−i2−22i2−i20000
χ512-22-2−2i2i−2i2i02-2022-2-2000000000−2i2i0000-22-222i−2i2i−2i000000000000000002−2−i2i2−22i2−i20000
χ522-22-2−2i2i−2i2i02-2022-2-2000000000−2i2i0000-22-222i−2i2i−2i00000000000000000−22i2−i22−2−i2i20000
χ5344-4-40000400-422−2222−2204-4000022−220022−2222−220000000000000000000000000000000000000
χ5444-4-40000400-422−2222−220-44000022−2200−2222−22220000000000000000000000000000000000000
χ5544-4-40000400-4−2222−222204-40000−222200−2222−22220000000000000000000000000000000000000
χ5644-4-40000400-4−2222−22220-440000−22220022−2222−220000000000000000000000000000000000000
χ5744-4-40000-400422−2222−2200004i−4i0−2222002i2−2i2−2i22i20000000000000000000000000000000000000
χ5844-4-40000-400422−2222−220000−4i4i0−222200−2i22i22i2−2i20000000000000000000000000000000000000
χ5944-4-40000-4004−2222−222200004i−4i022−2200−2i22i22i2−2i20000000000000000000000000000000000000
χ6044-4-40000-4004−2222−22220000−4i4i022−22002i2−2i2−2i22i20000000000000000000000000000000000000
χ614-44-44i−4i4i−4i04-40-4-444000000000−4i4i00000000000000000000000000000000000000000
χ624-44-44i−4i−4i4i0-440000000000000000000022−22−22222i2−2i2−2i22i200000000000000000000000000000
χ634-44-44i−4i−4i4i0-4400000000000000000000−222222−22−2i22i22i2−2i200000000000000000000000000000
χ644-44-4−4i4i4i−4i0-440000000000000000000022−22−2222−2i22i22i2−2i200000000000000000000000000000
χ654-44-4−4i4i4i−4i0-4400000000000000000000−222222−222i2−2i2−2i22i200000000000000000000000000000
χ664-44-4−4i4i−4i4i04-40-4-4440000000004i−4i00000000000000000000000000000000000000000
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).