Finite Group Databasebeta

← Group #130430

Character table — Group #130430

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11112222222222222244444444888888888888888888888888161616161616161632323232
order122222444488888888224444442488888816161616161616161616161616161616224444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11-111-1-1
χ6111111111111111111-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-11-1-111
χ7111111111111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-1-1-111
χ8111111111111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1111-1-1
χ91111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1iiii−i−i−i−iiiii−i−i−i−i111-11-1-1-1i−ii−i
χ101111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-11-1111−ii−ii
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1−i−i−i−iiiii−i−i−i−iiiii111-11-1-1-1−ii−ii
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-11-1111i−ii−i
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-111iiii−i−i−i−i−i−i−i−iiiii1-11-1-11-11i−i−ii
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-111-11-1−iii−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-111−i−i−i−iiiiiiiii−i−i−i−i1-11-1-11-11−iii−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-111-11-1i−i−ii
χ1722222222222222222222-2-2-2-2-2-2-22-2-2-2-2220000000000000000000000000000
χ18222222222222222222-2-2-2-222-2-22-2-2-222-2-20000000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-20000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222220000000000000000000000000000
χ21222222-2-2-2-200000000222222-2-2-2-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ22222222-2-2-2-200000000222222-2-2-2-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ23222222-2-2-2-20000000022-2-2-2-2222-200000022−2−2−2−22222−2−2−2−222000000000000
χ24222222-2-2-2-20000000022-2-2-2-2222-2000000−2−22222−2−2−2−22222−2−2000000000000
χ25222222-2-2-2-200000000-2-222-2-2-2-222000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ26222222-2-2-2-200000000-2-222-2-2-2-222000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ27222222-2-2-2-200000000-2-2-2-22222-2200000022−2−2−2−222−2−22222−2−2000000000000
χ28222222-2-2-2-200000000-2-2-2-22222-22000000−2−22222−2−222−2−2−2−222000000000000
χ292222-2-2-2-22222-2-2-2-222002-2002-2002-2000000000000000000000200-2-2020000
χ302222-2-2-2-22222-2-2-2-222002-2002-2002-2000000000000000000000-200220-20000
χ312222-2-2-2-22222-2-2-2-22200-2200-2200-220000000000000000000020-2-200200000
χ322222-2-2-2-22222-2-2-2-22200-2200-2200-2200000000000000000000-202200-200000
χ332222-2-2-2-222-2-22222-2-2002-2002-200-220000000000000000000020-2200-200000
χ342222-2-2-2-222-2-22222-2-2002-2002-200-2200000000000000000000-202-200200000
χ352222-2-2-2-222-2-22222-2-200-2200-22002-2000000000000000000000200-220-20000
χ362222-2-2-2-222-2-22222-2-200-2200-22002-2000000000000000000000-2002-2020000
χ374444-4-444-4-400000000004-400-44000000000000000000000000000000000000
χ384444-4-444-4-40000000000-44004-4000000000000000000000000000000000000
χ3944-4-4004i−4i002i2−2i22222−22−222i2−2i20000000000000000000000002ζ−2ζ2ζ5−2ζ52ζ3−2ζ32ζ7−2ζ7000000000000
χ4044-4-4004i−4i002i2−2i22222−22−222i2−2i2000000000000000000000000−2ζ2ζ−2ζ52ζ5−2ζ32ζ3−2ζ72ζ7000000000000
χ4144-4-4004i−4i00−2i22i2−22−222222−2i22i20000000000000000000000002ζ5−2ζ5−2ζ2ζ−2ζ72ζ72ζ3−2ζ3000000000000
χ4244-4-4004i−4i00−2i22i2−22−222222−2i22i2000000000000000000000000−2ζ52ζ52ζ−2ζ2ζ7−2ζ7−2ζ32ζ3000000000000
χ4344-4-400−4i4i002i2−2i2−22−2222222i2−2i20000000000000000000000002ζ3−2ζ3−2ζ72ζ7−2ζ2ζ2ζ5−2ζ5000000000000
χ4444-4-400−4i4i002i2−2i2−22−2222222i2−2i2000000000000000000000000−2ζ32ζ32ζ7−2ζ72ζ−2ζ−2ζ52ζ5000000000000
χ4544-4-400−4i4i00−2i22i22222−22−22−2i22i20000000000000000000000002ζ7−2ζ72ζ3−2ζ32ζ5−2ζ52ζ−2ζ000000000000
χ4644-4-400−4i4i00−2i22i22222−22−22−2i22i2000000000000000000000000−2ζ72ζ7−2ζ32ζ3−2ζ52ζ5−2ζ2ζ000000000000
χ474-44-44-400002i2−2i22i2−2i22i2−2i2−2i22i200004i−4i00000022−22000000000000000000000000000000
χ484-44-44-400002i2−2i22i2−2i22i2−2i2−2i22i20000−4i4i000000−2222000000000000000000000000000000
χ494-44-44-40000−2i22i2−2i22i2−2i22i22i2−2i200004i−4i000000−2222000000000000000000000000000000
χ504-44-44-40000−2i22i2−2i22i2−2i22i22i2−2i20000−4i4i00000022−22000000000000000000000000000000
χ514-44-4-4400002i2−2i2−2i22i2−2i22i2−2i22i24-40000000000002i2−2i20000000000000000000000000000
χ524-44-4-4400002i2−2i2−2i22i2−2i22i2−2i22i2-44000000000000−2i22i20000000000000000000000000000
χ534-44-4-440000−2i22i22i2−2i22i2−2i22i2−2i24-4000000000000−2i22i20000000000000000000000000000
χ544-44-4-440000−2i22i22i2−2i22i2−2i22i2−2i2-440000000000002i2−2i20000000000000000000000000000
χ554-4-4400004-4004i−4i−4i4i0000000000000000002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ600000000000000000000
χ564-4-4400004-4004i−4i−4i4i000000000000000000−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ600000000000000000000
χ574-4-4400004-400−4i4i4i−4i0000000000000000002ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ200000000000000000000
χ584-4-4400004-400−4i4i4i−4i000000000000000000−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ200000000000000000000
χ594-4-440000-44440000-4-400000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ604-4-440000-44440000-4-40000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ614-4-440000-44-4-400004400000000000000002-2-222-2-2200000000000000000000
χ624-4-440000-44-4-40000440000000000000000-222-2-222-200000000000000000000

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