Finite Group Databasebeta

← Group #495991

Character table — Group #495991

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444888888884444444488881616161616161616161616161616161622224444444444448888161616161616161644444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1
χ911111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ1111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111
χ1211111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111
χ17111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i11-1-11-1i−iii−i−i11-1-1i−ii−i1-11-1
χ18111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii−i−iii-1-1111-1i−iii−i−i11-1-1−ii−ii-11-11
χ19111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−iii−i−i11-1-11-1i−i−i−iii-1-111−ii−ii-11-11
χ20111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-11-1i−ii−i1-1ii−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii−i−iii-1-1111-1i−i−i−iii-1-111i−ii−i1-11-1
χ21111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i−i−iii-1-111-11−ii−i−iii-1-111i−i−ii1-1-11
χ22111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i11-1-1-11−ii−i−iii-1-111−iii−i-111-1
χ23111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−i−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i−i−iii-1-111-11−iiii−i−i11-1-1−iii−i-111-1
χ24111-1-1-1-11ii−i−iii−i−i11-1-111-1-111-1-1-11−ii−ii-11ii−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iiiii−i−i11-1-1-11−iiii−i−i11-1-1i−i−ii1-1-11
χ25111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii−i−iii11-1-11-1−iiii−i−i-1-111i−ii−i-11-11
χ26111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−iii−i−i-1-1111-1−iiii−i−i-1-111−ii−ii1-11-1
χ27111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii11-1-11-1−ii−i−iii11-1-1−ii−ii1-11-1
χ28111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-11-1−ii−ii1-1−i−iii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−iii−i−i-1-1111-1−ii−i−iii11-1-1i−ii−i-11-11
χ29111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-1−i−iiiii−i−i-1-111-11i−i−i−iii11-1-1i−i−ii-111-1
χ30111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i−i−iii11-1-1-11i−i−i−iii11-1-1−iii−i1-1-11
χ31111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iiiii−i−i-1-111-11i−iii−i−i-1-111−iii−i1-1-11
χ32111-1-1-1-11−i−iii−i−iii11-1-111-1-111-1-1-11i−ii−i-11−i−iii−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii11-1-1-11i−iii−i−i-1-111i−i−ii-111-1
χ3322222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-2-2-20000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022220000000000000000
χ35222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-2000022−2−222−2−222−2−222−2−2000000000000000000002−22−22−22−200000000
χ36222222222222-2-2-2-2-2-2-2-20000000022-2-222-2-20000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ37222222222222-2-2-2-2-2-2-2-200000000-2-222-2-222000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ38222222222222-2-2-2-2-2-2-2-200000000-2-222-2-2220000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
χ3922222222-2-2-2-22222-2-2-2-2000000002222-2-2-2-2000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ4022222222-2-2-2-22222-2-2-2-2000000002222-2-2-2-20000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ4122222222-2-2-2-22222-2-2-2-200000000-2-2-2-22222000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ4222222222-2-2-2-22222-2-2-2-200000000-2-2-2-222220000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-222222200000000000000000000000000000000-2-2220000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222-2-222220000000000000000000000000000000022-2-20000000000000000
χ45222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2-2-222-2-2222-22i−2i2i−2i2-2−2i−2i2i2i00000000000000000000000000000000-22−2i2i0000000000000000
χ46222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2-2-222-2-222-22−2i2i−2i2i-22−2i−2i2i2i000000000000000000000000000000002-22i−2i0000000000000000
χ47222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-222000000002-2−2i2i2i−2i-220000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000i2−i2−i2i22−2−2200000000
χ48222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-222000000002-2−2i2i2i−2i-220000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000−i2i2i2−i2−222−200000000
χ49222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-22200000000-222i−2i−2i2i2-20000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000−i2i2i2−i2−222−200000000
χ50222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-22200000000-222i−2i−2i2i2-20000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000i2−i2−i2i22−2−2200000000
χ51222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-222000000002-22i−2i−2i2i-220000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000i2−i2−i2i2−222−200000000
χ52222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-222000000002-22i−2i−2i2i-220000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000−i2i2i2−i22−2−2200000000
χ53222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22200000000-22−2i2i2i−2i2-20000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000−i2i2i2−i22−2−2200000000
χ54222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22200000000-22−2i2i2i−2i2-20000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000i2−i2−i2i2−222−200000000
χ55222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2-2-222-2-2222-2−2i2i−2i2i2-22i2i−2i−2i00000000000000000000000000000000-222i−2i0000000000000000
χ56222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2-2-222-2-222-222i−2i2i−2i-222i2i−2i−2i000000000000000000000000000000002-2−2i2i0000000000000000
χ5722-222-2-2-22-22-22-22-22-22-22222-2-2-2-2000000002-22-200000000000000002-22-22-22-20000000000000000000000000000
χ5822-222-2-2-22-22-22-22-22-22-22222-2-2-2-2000000002-22-20000000000000000-22-22-22-220000000000000000000000000000
χ5922-222-2-2-22-22-22-22-22-22-2-2-2-2-2222200000000-22-220000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ6022-222-2-2-22-22-22-22-22-22-2-2-2-2-2222200000000-22-22000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ6122-222-2-2-2-22-22-22-222-22-22222-2-2-2-200000000-22-2200000000000000002-22-2-22-220000000000000000000000000000
χ6222-222-2-2-2-22-22-22-222-22-22222-2-2-2-200000000-22-220000000000000000-22-222-22-20000000000000000000000000000
χ6322-222-2-2-2-22-22-22-222-22-2-2-2-2-22222000000002-22-20000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ6422-222-2-2-2-22-22-22-222-22-2-2-2-2-22222000000002-22-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ6522-2-2-222-22i−2i−2i2i2i−2i−2i2i2-2-2222-2-2-2-222000000002i−2i−2i2i00000000000000002-2-222i−2i−2i2i0000000000000000000000000000
χ6622-2-2-222-22i−2i−2i2i2i−2i−2i2i2-2-2222-2-2-2-222000000002i−2i−2i2i0000000000000000-222-2−2i2i2i−2i0000000000000000000000000000
χ6722-2-2-222-22i−2i−2i2i2i−2i−2i2i2-2-22-2-22222-2-200000000−2i2i2i−2i0000000000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ6822-2-2-222-22i−2i−2i2i2i−2i−2i2i2-2-22-2-22222-2-200000000−2i2i2i−2i000000000000000000000000-222-22i−2i−2i2i00000000000000000000
χ6922-2-2-222-2−2i2i2i−2i−2i2i2i−2i2-2-2222-2-2-2-22200000000−2i2i2i−2i00000000000000002-2-22−2i2i2i−2i0000000000000000000000000000
χ7022-2-2-222-2−2i2i2i−2i−2i2i2i−2i2-2-2222-2-2-2-22200000000−2i2i2i−2i0000000000000000-222-22i−2i−2i2i0000000000000000000000000000
χ7122-2-2-222-2−2i2i2i−2i−2i2i2i−2i2-2-22-2-22222-2-2000000002i−2i−2i2i0000000000000000000000002-2-222i−2i−2i2i00000000000000000000
χ7222-2-2-222-2−2i2i2i−2i−2i2i2i−2i2-2-22-2-22222-2-2000000002i−2i−2i2i000000000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ7344-444-4-4-44-44-4-44-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ7444-444-4-4-4-44-444-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-44i−4i−4i4i−4i4i4i−4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4−4i4i4i−4i4i−4i−4i4i-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-400000000000022−2222−2222−2222−220000000000002ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000000000000000000000
χ784-444-44-4-400000000000022−2222−2222−2222−22000000000000−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000000000000000000000
χ794-444-44-4-4000000000000−2222−2222−2222−22220000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ700000000000000000000000000000000000000000000
χ804-444-44-4-4000000000000−2222−2222−2222−2222000000000000−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ700000000000000000000000000000000000000000000
χ814-44-44-44-400000000000022−22−222222−22−22220000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000000000
χ824-44-44-44-400000000000022−22−222222−22−2222000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000000000
χ834-44-44-44-4000000000000−222222−22−222222−220000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000000000
χ844-44-44-44-4000000000000−222222−22−222222−22000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000000000
χ854-4-44-4-44400000000000022−2222−22−2222−2222000000000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000000
χ864-4-44-4-44400000000000022−2222−22−2222−222200000000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000000
χ874-4-44-4-444000000000000−2222−222222−2222−22000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000000
χ884-4-44-4-444000000000000−2222−222222−2222−2200000000000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000000
χ894-4-4-444-4400000000000022−22−2222−222222−22000000000000000000002ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ7000000000000000000000000000000000000
χ904-4-4-444-4400000000000022−22−2222−222222−2200000000000000000000−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7000000000000000000000000000000000000
χ914-4-4-444-44000000000000−222222−2222−22−2222000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5000000000000000000000000000000000000
χ924-4-4-444-44000000000000−222222−2222−22−222200000000000000000000−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ5000000000000000000000000000000000000

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