Finite Group Databasebeta

← Group #72320738

Character table — Group #72320738

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113
size11222222244444444444488888888888888888888888888888888161616161616161616161616323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232323232
order12222444444448888888824448888888888881616161616161616161616161616161688881616161616161616224444448888888888888888161616161616161632323232323232323232323232323232
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ511111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ811111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ9111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ10111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ11111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ12111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ13111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ14111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ15111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ16111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ17111111111-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1ii−i−i111111-1-111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ18111111111-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1ii−i−i11-1-1-1-1-1-111-1-11111ii−i−iii−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii
χ19111111111-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1ii−i−i-1-1111111-1-111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ20111111111-1-1-1-11111-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1ii−i−i-1-1-1-1-1-111-1-1111111−i−iii−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i
χ21111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1−i−iii111111-1-111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ22111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1−i−iii11-1-1-1-1-1-111-1-11111−i−iii−i−iiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i
χ23111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1−i−iii-1-1111111-1-111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ24111111111-1-1-1-11111-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1−i−iii-1-1-1-1-1-111-1-1111111ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii
χ25111111111-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111−i−iii1111-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ26111111111-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111−i−iii11-1-111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ27111111111-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111−i−iii-1-111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ28111111111-1-1-1-11111-1-1-1-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111−i−iii-1-1-1-1111111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ29111111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111ii−i−i1111-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ30111111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111ii−i−i11-1-111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ31111111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111ii−i−i-1-111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ32111111111-1-1-1-11111-1-1-1-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111ii−i−i-1-1-1-1111111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ332222222222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3422222222222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ35222222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ36222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ37222222222-2-2-2-22222-2-2-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2-2-222222i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000
χ38222222222-2-2-2-22222-2-2-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-2-2-22222−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000000000000000000000
χ39222222222-2-2-2-22222-2-2-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2-2-22222−2i−2i2i2i22-2-22i2i−2i−2i000000000000000000000000000000000000000000000000
χ40222222222-2-2-2-22222-2-2-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-2-2-222222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000
χ41222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ322-2-22i2i−2i−2i0000000000000000000000000000000000000000000000002i−2i2-200002ζ3−2ζ32ζ−2ζ
χ42222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ322-2-22i2i−2i−2i000000000000000000000000000000000000000000000000−2i2i-220000−2ζ32ζ3−2ζ2ζ
χ43222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3-2-222−2i−2i2i2i000000000000000000000000000000000000000000002-22i−2i00002ζ−2ζ2ζ3−2ζ30000
χ44222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3-2-222−2i−2i2i2i00000000000000000000000000000000000000000000-22−2i2i0000−2ζ2ζ−2ζ32ζ30000
χ45222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3-2-222−2i−2i2i2i000000000000000000000000000000000000000000002-22i−2i0000−2ζ2ζ−2ζ32ζ30000
χ46222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3-2-222−2i−2i2i2i00000000000000000000000000000000000000000000-22−2i2i00002ζ−2ζ2ζ3−2ζ30000
χ47222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ322-2-22i2i−2i−2i0000000000000000000000000000000000000000000000002i−2i2-20000−2ζ32ζ3−2ζ2ζ
χ48222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ322-2-22i2i−2i−2i000000000000000000000000000000000000000000000000−2i2i-2200002ζ3−2ζ32ζ−2ζ
χ49222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ22-2-2−2i−2i2i2i0000000000000000000000000000000000000000000000002i−2i-220000−2ζ2ζ−2ζ32ζ3
χ50222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ22-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000−2i2i2-200002ζ−2ζ2ζ3−2ζ3
χ51222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-2-2222i2i−2i−2i000000000000000000000000000000000000000000002-2−2i2i00002ζ3−2ζ32ζ−2ζ0000
χ52222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ-2-2222i2i−2i−2i00000000000000000000000000000000000000000000-222i−2i0000−2ζ32ζ3−2ζ2ζ0000
χ53222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ-2-2222i2i−2i−2i000000000000000000000000000000000000000000002-2−2i2i0000−2ζ32ζ3−2ζ2ζ0000
χ54222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ-2-2222i2i−2i−2i00000000000000000000000000000000000000000000-222i−2i00002ζ3−2ζ32ζ−2ζ0000
χ55222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ22-2-2−2i−2i2i2i0000000000000000000000000000000000000000000000002i−2i-2200002ζ−2ζ2ζ3−2ζ3
χ56222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ22-2-2−2i−2i2i2i000000000000000000000000000000000000000000000000−2i2i2-20000−2ζ2ζ−2ζ32ζ3
χ5722-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2-22-22i−2i2i−2i000000000000000000002-22i−2i00002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ5822-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2-22-22i−2i2i−2i00000000000000000000-22−2i2i0000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ5922-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ-22-22−2i2i−2i2i0000000000002-200002i−2i0000000000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ6022-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ-22-22−2i2i−2i2i000000000000-220000−2i2i000000000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ6122-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ-22-22−2i2i−2i2i0000000000002-200002i−2i000000000000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ6222-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ-22-22−2i2i−2i2i000000000000-220000−2i2i0000000000002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ6322-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2-22-22i−2i2i−2i000000000000000000002-22i−2i0000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6422-22-22-2-222i−2i−2i2i-222-2−2i2i2i−2i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2-22-22i−2i2i−2i00000000000000000000-22−2i2i00002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ6522-22-22-2-22−2i2i2i−2i-222-22i−2i−2i2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-22-2−2i2i−2i2i000000000000000000002-2−2i2i00002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ6622-22-22-2-22−2i2i2i−2i-222-22i−2i−2i2i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-22-2−2i2i−2i2i00000000000000000000-222i−2i0000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.