Finite Group Databasebeta

← Group #367244

Character table — Group #367244

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222224444444444444444444444448888888888888888444444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ10111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ11111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ17111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1i−i1-11-1i−i
χ18111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i-1-111-1-111−i−iii−i−iii11-1-111-1-1−ii-11-11−ii
χ19111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i11-1-111-1-1ii−i−iii−i−i-1-111-1-111−ii-11-11−ii
χ20111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111i−i1-11-1i−i
χ21111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii11-1-1-1-111ii−i−i−i−iii11-1-1-1-111i−i1-1-11−ii
χ22111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iii-1-11111-1-1−i−iiiii−i−i11-1-1-1-111−ii-111-1i−i
χ23111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−ii-111-1i−i
χ24111-1-111-1-1-1-111-11-111-1-111-1-1iiii−i−i−i−i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-11111-1-1−i−iiiii−i−i-1-11111-1-1i−i1-1-11−ii
χ25111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii11-1-111-1-1−i−iii−i−iii-1-111-1-111i−i-11-11i−i
χ26111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111−ii1-11-1−ii
χ27111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−ii1-11-1−ii
χ28111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii-1-111-1-111ii−i−iii−i−i11-1-111-1-1i−i-11-11i−i
χ29111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-1-111−i−iiiii−i−i-1-11111-1-1i−i-111-1−ii
χ30111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-11111-1-1ii−i−i−i−iii-1-11111-1-1−ii1-1-11i−i
χ31111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−ii1-1-11i−i
χ32111-1-111-1-1-1-111-11-111-1-111-1-1−i−i−i−iiiii-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-11111-1-1ii−i−i−i−iii11-1-1-1-111i−i-111-1−ii
χ332222222222222222-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-200000000000000002-22-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-222220000000000000000-22-2200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-20000000000000000-22-2200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2222200000000000000002-22-200000000000000000000000000000000
χ37222222-222-2-2-2-2-2-2-22-22-22-22-22-22-22-22-2000000000000000022-2-222-2-20000000000000000000000002-22-200000000
χ38222222-222-2-2-2-2-2-2-22-22-22-22-22-22-22-22-20000000000000000-2-222-2-222000000000000000000000000-22-2200000000
χ39222222-222-2-2-2-2-2-2-22-22-22-22-2-22-22-22-22000000000000000022-2-222-2-2000000000000000000000000-22-2200000000
χ40222222-222-2-2-2-2-2-2-22-22-22-22-2-22-22-22-220000000000000000-2-222-2-2220000000000000000000000002-22-200000000
χ41222222-222-2-2-2-2-2-2-2-22-22-22-222-2-222-2-220000000022-2-222-2-200000000000000000000000000002-22-2000000000000
χ42222222-222-2-2-2-2-2-2-2-22-22-22-222-2-222-2-2200000000-2-222-2-2220000000000000000000000000000-22-22000000000000
χ43222222-222-2-2-2-2-2-2-2-22-22-22-22-222-2-222-20000000022-2-222-2-20000000000000000000000000000-22-22000000000000
χ44222222-222-2-2-2-2-2-2-2-22-22-22-22-222-2-222-200000000-2-222-2-22200000000000000000000000000002-22-2000000000000
χ45222-2-222-2-2-2-222-22-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i22-2-2-2-22200000000000000002i−2i−2i2i00000000000000000000000000000000
χ46222-2-222-2-2-2-222-22-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i-2-22222-2-20000000000000000−2i2i2i−2i00000000000000000000000000000000
χ47222-2-222-2-2-2-222-22-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i22-2-2-2-2220000000000000000−2i2i2i−2i00000000000000000000000000000000
χ48222-2-222-2-2-2-222-22-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i-2-22222-2-200000000000000002i−2i−2i2i00000000000000000000000000000000
χ49222-2-22-2-2-222-2-22-222-2-222-2-222i−2i2i−2i−2i2i−2i2i00000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000002-2-2200000000
χ50222-2-22-2-2-222-2-22-222-2-222-2-222i−2i2i−2i−2i2i−2i2i0000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000-222-200000000
χ51222-2-22-2-2-222-2-22-222-2-222-2-22−2i2i−2i2i2i−2i2i−2i00000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000-222-200000000
χ52222-2-22-2-2-222-2-22-222-2-222-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-2-2200000000
χ53222-2-22-2-2-222-2-22-22-222-2-222-22i−2i−2i2i−2i2i2i−2i000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000002-2-22000000000000
χ54222-2-22-2-2-222-2-22-22-222-2-222-22i−2i−2i2i−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000-222-2000000000000
χ55222-2-22-2-2-222-2-22-22-222-2-222-2−2i2i2i−2i2i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000-222-2000000000000
χ56222-2-22-2-2-222-2-22-22-222-2-222-2−2i2i2i−2i2i−2i−2i2i00000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000002-2-22000000000000
χ572-2-22222-2-2-2-2-2-22222222-2-2-2-2000000002-22-22-22-2000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ582-2-22222-2-2-2-2-2-22222222-2-2-2-2000000002-22-22-22-200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ592-2-22222-2-2-2-2-2-22222222-2-2-2-200000000-22-22-22-22000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ602-2-22222-2-2-2-2-2-22222222-2-2-2-200000000-22-22-22-2200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ612-2-22222-2-2-2-2-2-2222-2-2-2-22222000000002-22-2-22-2200000000000000000000000000002-22-22-22-20000000000000000
χ622-2-22222-2-2-2-2-2-2222-2-2-2-22222000000002-22-2-22-220000000000000000000000000000-22-22-22-220000000000000000
χ632-2-22222-2-2-2-2-2-2222-2-2-2-2222200000000-22-222-22-200000000000000000000000000002-22-2-22-220000000000000000
χ642-2-22222-2-2-2-2-2-2222-2-2-2-2222200000000-22-222-22-20000000000000000000000000000-22-222-22-20000000000000000
χ652-2-2-2-2222222-2-2-22-222-2-2-2-222000000002-2-222-2-22000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ662-2-2-2-2222222-2-2-22-222-2-2-2-222000000002-2-222-2-2200000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ672-2-2-2-2222222-2-2-22-222-2-2-2-22200000000-222-2-222-2000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ682-2-2-2-2222222-2-2-22-222-2-2-2-22200000000-222-2-222-200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ692-2-2-2-2222222-2-2-22-2-2-22222-2-2000000002-2-22-222-200000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ702-2-2-2-2222222-2-2-22-2-2-22222-2-2000000002-2-22-222-20000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ712-2-2-2-2222222-2-2-22-2-2-22222-2-200000000-222-22-2-2200000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ722-2-2-2-2222222-2-2-22-2-2-22222-2-200000000-222-22-2-220000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ7344-44-4-444-44-44-44-4-40000000000000000000000000000000022−2222−2222−2222−22000000000000000000000000000000000000
χ7444-44-4-444-44-44-44-4-400000000000000000000000000000000−2222−2222−2222−2222000000000000000000000000000000000000
χ7544-44-4-4-44-4-44-44-4440000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ7644-44-4-4-44-4-44-44-44400000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ7744-4-44-44-44-444-4-4-44000000000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ7844-4-44-44-44-444-4-4-4400000000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ7944-4-44-4-4-444-4-4444-4000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ8044-4-44-4-4-444-4-4444-400000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ814-444-4-44-44-44-444-4-400000000000000000000000022−2222−2222−2222−2200000000000000000000000000000000000000000000
χ824-444-4-44-44-44-444-4-4000000000000000000000000−2222−2222−2222−222200000000000000000000000000000000000000000000
χ834-444-4-4-4-444-44-4-44400000000000000000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ844-444-4-4-4-444-44-4-444000000000000000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ854-44-44-444-44-4-44-4-440000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ864-44-44-444-44-4-44-4-44000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ874-44-44-4-44-4-444-444-40000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ884-44-44-4-44-4-444-444-4000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ894-4-4444-4-4-44444-4-4-44-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-44444-4-4-4-44-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-4-44-444-4-4444-444-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-44-444-4-4444-44-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000

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