Finite Group Databasebeta

← Group #367441

Character table — Group #367441

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222224444444422224444444444448888888888888888444444444444444444448888888844444444
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
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
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
χ11111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-111-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ171111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−ii−ii−iii−i−i11-1-111-1-1ii−i−i11-1-1ii−i−i1-11-1i−ii−i
χ181111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−ii−ii−i−i−iii-1-111-1-111−i−iii11-1-1ii−i−i-11-11−ii−ii
χ191111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiii−ii−iii−i−i-1-111-1-111ii−i−i-1-111−i−iii1-11-1−ii−ii
χ201111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiiii−ii−i−i−iii11-1-111-1-1−i−iii-1-111−i−iii-11-11i−ii−i
χ211111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−iiii−i−i-1-111-1-111ii−i−i11-1-1−i−iii-11-11i−ii−i
χ221111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−ii−i−iii11-1-111-1-1−i−iii11-1-1−i−iii1-11-1−ii−ii
χ231111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−ii−iiii−i−i11-1-111-1-1ii−i−i-1-111ii−i−i-11-11−ii−ii
χ241111-1-1-1-1-1111-1-11-111-1-1-111-111-1-111-1-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−i−ii−ii−i−iii-1-111-1-111−i−iii-1-111ii−i−i1-11-1i−ii−i
χ251111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−ii−iiii−i−i11-1-1-1-111−i−iii-1-111−i−iii1-1-11−iii−i
χ261111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−ii−ii−i−iii-1-11111-1-1ii−i−i-1-111−i−iii-111-1i−i−ii
χ271111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−ii−iiii−i−i-1-11111-1-1−i−iii11-1-1ii−i−i1-1-11i−i−ii
χ281111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−ii−ii−i−iii11-1-1-1-111ii−i−i11-1-1ii−i−i-111-1−iii−i
χ291111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiiii−ii−iii−i−i-1-11111-1-1−i−iii-1-111ii−i−i-111-1−iii−i
χ301111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiiii−ii−i−i−iii11-1-1-1-111ii−i−i-1-111ii−i−i1-1-11i−i−ii
χ311111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111−i−iii−i−iii-1-1-1-11111iiii−i−i−i−ii−ii−iii−i−i11-1-1-1-111−i−iii11-1-1−i−iii-111-1i−i−ii
χ321111-1-1-1-1-1111-1-11-111-1-1-111-1-1-111-1-111−i−iii−i−iii-1-1-1-11111iiii−i−i−i−ii−ii−i−i−iii-1-11111-1-1ii−i−i11-1-1−i−iii1-1-11−iii−i
χ332222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000022-2-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000-2-22200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000-2-22200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000022-2-200000000000000000000000000000000
χ372222-2-2-2-2-2222-2-22-2-2-2222-2-2222-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00000000000000000000000000000000
χ382222-2-2-2-2-2222-2-22-2-2-2222-2-2222-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00000000000000000000000000000000
χ392222-2-2-2-2-2222-2-22-2-2-2222-2-22-2-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i00000000000000000000000000000000
χ402222-2-2-2-2-2222-2-22-2-2-2222-2-22-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i00000000000000000000000000000000
χ41222-22222-22-2-2-2-2-2-2222-2-2-2-222-22-22-22-2000000000000000022-2-222-2-20000000000000000000000002-22-200000000
χ42222-22222-22-2-2-2-2-2-2222-2-2-2-222-22-22-22-20000000000000000-2-222-2-222000000000000000000000000-22-2200000000
χ43222-22222-22-2-2-2-2-2-2222-2-2-2-22-22-22-22-22000000000000000022-2-222-2-2000000000000000000000000-22-2200000000
χ44222-22222-22-2-2-2-2-2-2222-2-2-2-22-22-22-22-220000000000000000-2-222-2-2220000000000000000000000002-22-200000000
χ45222-22222-22-2-2-2-2-2-2-2-2-22222-22-22-2-22-220000000022-2-222-2-200000000000000000000000000002-22-2000000000000
χ46222-22222-22-2-2-2-2-2-2-2-2-22222-22-22-2-22-2200000000-2-222-2-2220000000000000000000000000000-22-22000000000000
χ47222-22222-22-2-2-2-2-2-2-2-2-22222-2-22-222-22-20000000022-2-222-2-20000000000000000000000000000-22-22000000000000
χ48222-22222-22-2-2-2-2-2-2-2-2-22222-2-22-222-22-200000000-2-222-2-22200000000000000000000000000002-22-2000000000000
χ49222-2-2-2-2-222-2-222-2222-222-2-2-22-2-222-2-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000002i−2i−2i2i00000000
χ50222-2-2-2-2-222-2-222-2222-222-2-2-22-2-222-2-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000−2i2i2i−2i00000000
χ51222-2-2-2-2-222-2-222-2222-222-2-2-2-222-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i00000000
χ52222-2-2-2-2-222-2-222-2222-222-2-2-2-222-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i−2i2i00000000
χ53222-2-2-2-2-222-2-222-22-2-22-2-22222-2-22-222-20000000022-2-2-2-22200000000000000000000000000002-2-22000000000000
χ54222-2-2-2-2-222-2-222-22-2-22-2-22222-2-22-222-200000000-2-22222-2-20000000000000000000000000000-222-2000000000000
χ55222-2-2-2-2-222-2-222-22-2-22-2-2222-222-22-2-220000000022-2-2-2-2220000000000000000000000000000-222-2000000000000
χ56222-2-2-2-2-222-2-222-22-2-22-2-2222-222-22-2-2200000000-2-22222-2-200000000000000000000000000002-2-22000000000000
χ572-2-2222-2-2222-22-2-2-22-2-22-22-220000000000000000000000002-22-22-22-20000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ582-2-2222-2-2222-22-2-2-22-2-22-22-220000000000000000000000002-22-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ592-2-2222-2-2222-22-2-2-22-2-22-22-22000000000000000000000000-22-22-22-220000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ602-2-2222-2-2222-22-2-2-22-2-22-22-22000000000000000000000000-22-22-22-22000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ612-2-22-2-222-222-2-22-222-22-222-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000002i−2i−2i2i-222-20000000000000000
χ622-2-22-2-222-222-2-22-222-22-222-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000−2i2i2i−2i2-2-220000000000000000
χ632-2-22-2-222-222-2-22-222-22-222-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000002i−2i−2i2i2-2-220000000000000000
χ642-2-22-2-222-222-2-22-222-22-222-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000−2i2i2i−2i-222-20000000000000000
χ652-2-2-222-2-2-22-22-22222-2-2-22-2220000000000000000000000002-2-222-2-2200002-22-22-22-2000000000000000000000000
χ662-2-2-222-2-2-22-22-22222-2-2-22-2220000000000000000000000002-2-222-2-220000-22-22-22-22000000000000000000000000
χ672-2-2-222-2-2-22-22-22222-2-2-22-222000000000000000000000000-222-2-222-200002-22-2-22-22000000000000000000000000
χ682-2-2-222-2-2-22-22-22222-2-2-22-222000000000000000000000000-222-2-222-20000-22-222-22-2000000000000000000000000
χ692-2-2-2-2-22222-222-22-22-222-2-22-20000000000000000000000002i−2i−2i2i−2i2i2i−2i00002i−2i−2i2i2-2-22000000000000000000000000
χ702-2-2-2-2-22222-222-22-22-222-2-22-20000000000000000000000002i−2i−2i2i−2i2i2i−2i0000−2i2i2i−2i-222-2000000000000000000000000
χ712-2-2-2-2-22222-222-22-22-222-2-22-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i00002i−2i−2i2i-222-2000000000000000000000000
χ722-2-2-2-2-22222-222-22-22-222-2-22-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000−2i2i2i−2i2-2-22000000000000000000000000
χ7344-444-44-44-4-44-44-4-400000000000000004-44-400000000000000000000000000000000000000000000000000000000
χ7444-444-44-44-4-44-44-4-40000000000000000-44-4400000000000000000000000000000000000000000000000000000000
χ7544-44-44-44-4-4-444-4-4400000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ7644-44-44-44-4-4-444-4-440000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ7744-4-44-44-4-4-44-44-444000000000000000000004-44-40000000000000000000000000000000000000000000000000000
χ7844-4-44-44-4-4-44-44-44400000000000000000000-44-440000000000000000000000000000000000000000000000000000
χ7944-4-4-44-444-44-4-444-4000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ8044-4-4-44-444-44-4-444-400000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ814-4444-4-444-4-4-4-4-4440000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ824-4444-4-444-4-4-4-4-444000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ834-444-444-4-4-4-4-4444-40000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ844-444-444-4-4-4-4-4444-4000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ854-44-44-4-44-4-44444-4-40000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ864-44-44-4-44-4-44444-4-4000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ874-44-4-444-44-444-4-4-440000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ884-44-4-444-44-444-4-4-44000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ894-4-4444-4-4444-44-4-4-4-444-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ904-4-44-4-444-444-4-44-44-44-44-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-444-4-4-44-44-4444-4444-44-4-400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4-44444-444-44-4-44-4-444-4400000000000000000000000000000000000000000000000000000000000000000000

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