Finite Group Databasebeta

← Group #377539

Character table — Group #377539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444444444444444444442222444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ121111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ141111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ151111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ161111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ171111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1iiii−i−i−i−i11-1-1ii−i−i11-1-111-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1ii−i−ii−i1-1i−i1-1
χ181111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1iiii−i−i−i−i11-1-1ii−i−i11-1-111-1-1ii−i−iii−i−i11-1-1−i−iii-1-111-1-111−i−iii−ii-11−ii-11
χ191111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1-1-111−i−iii−i−iii-1-111ii−i−i11-1-111-1-1ii−i−i−ii-11−ii-11
χ201111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1-1-111−i−iii−i−iii-1-111−i−iii-1-111-1-111−i−iiii−i1-1i−i1-1
χ211111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1−i−i−i−iiiii-1-111ii−i−i-1-11111-1-1−i−iiiii−i−i-1-111ii−i−i11-1-1-1-111−i−iiii−i-11−ii1-1
χ221111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1−i−i−i−iiiii-1-111ii−i−i-1-11111-1-1−i−iiiii−i−i-1-111−i−iii-1-11111-1-1ii−i−i−ii1-1i−i-11
χ231111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1−i−i−i−iiiii-1-111ii−i−i-1-111-1-111ii−i−i−i−iii11-1-1ii−i−i11-1-1-1-111−i−iii−ii1-1i−i-11
χ241111-1-111-1-1-1-11-1-11111-1-1-1iiii−i−i−i−i1-1−i−i−i−iiiii-1-111ii−i−i-1-111-1-111ii−i−i−i−iii11-1-1−i−iii-1-11111-1-1ii−i−ii−i-11−ii1-1
χ251111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1iiii−i−i−i−i-1-111−i−iii-1-11111-1-1ii−i−i−i−iii-1-111ii−i−i-1-11111-1-1−i−iiii−i1-1−ii-11
χ261111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1iiii−i−i−i−i-1-111−i−iii-1-11111-1-1ii−i−i−i−iii-1-111−i−iii11-1-1-1-111ii−i−i−ii-11i−i1-1
χ271111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1iiii−i−i−i−i-1-111−i−iii-1-111-1-111−i−iiiii−i−i11-1-1ii−i−i-1-11111-1-1−i−iii−ii-11i−i1-1
χ281111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1iiii−i−i−i−i-1-111−i−iii-1-111-1-111−i−iiiii−i−i11-1-1−i−iii11-1-1-1-111ii−i−ii−i1-1−ii-11
χ291111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1−i−i−i−iiiii11-1-1−i−iii11-1-111-1-1−i−iii−i−iii11-1-1ii−i−i-1-111-1-111ii−i−ii−i-11i−i-11
χ301111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1−i−i−i−iiiii11-1-1−i−iii11-1-111-1-1−i−iii−i−iii11-1-1−i−iii11-1-111-1-1−i−iii−ii1-1−ii1-1
χ311111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1−i−i−i−iiiii11-1-1−i−iii11-1-1-1-111ii−i−iii−i−i-1-111ii−i−i-1-111-1-111ii−i−i−ii1-1−ii1-1
χ321111-1-111-1-1-1-11-1-11111-1-1-1−i−i−i−iiiii1-1−i−i−i−iiiii11-1-1−i−iii11-1-1-1-111ii−i−iii−i−i-1-111−i−iii11-1-111-1-1−i−iiii−i-11i−i-11
χ332222222222222222-2-2-2-2-2-222222222-2-222-2-222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-20000000000000000000000000000000000000000
χ372222-2-222-2-2-2-22-2-22-2-2-22222i2i2i2i−2i−2i−2i−2i-222i2i−2i−2i−2i−2i2i2i22-2-2−2i−2i2i2i-2-2220000000000000000000000000000000000000000
χ382222-2-222-2-2-2-22-2-22-2-2-22222i2i2i2i−2i−2i−2i−2i-22−2i−2i2i2i2i2i−2i−2i-2-222−2i−2i2i2i22-2-20000000000000000000000000000000000000000
χ392222-2-222-2-2-2-22-2-22-2-2-2222−2i−2i−2i−2i2i2i2i2i-222i2i−2i−2i−2i−2i2i2i-2-2222i2i−2i−2i22-2-20000000000000000000000000000000000000000
χ402222-2-222-2-2-2-22-2-22-2-2-2222−2i−2i−2i−2i2i2i2i2i-22−2i−2i2i2i2i2i−2i−2i22-2-22i2i−2i−2i-2-2220000000000000000000000000000000000000000
χ41222-22-22-2222-2-2-2-2-222-222-200000000-2-22-22-22-22-20000000000002-22-22-22-200000000000000000000000000000000
χ42222-22-22-2222-2-2-2-2-222-222-200000000-2-22-22-22-22-2000000000000-22-22-22-2200000000000000000000000000000000
χ43222-22-22-2222-2-2-2-2-222-222-200000000-2-2-22-22-22-220000000000002-22-2-22-2200000000000000000000000000000000
χ44222-22-22-2222-2-2-2-2-222-222-200000000-2-2-22-22-22-22000000000000-22-222-22-200000000000000000000000000000000
χ45222-22-22-2222-2-2-2-2-2-2-22-2-2200000000222-2-222-2-22000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ46222-22-22-2222-2-2-2-2-2-2-22-2-2200000000222-2-222-2-2200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ47222-22-22-2222-2-2-2-2-2-2-22-2-220000000022-222-2-222-2000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ48222-22-22-2222-2-2-2-2-2-2-22-2-220000000022-222-2-222-200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ49222-2-222-2-2-2-22-222-222-2-2-2200000000-222i−2i2i−2i−2i2i−2i2i0000000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ50222-2-222-2-2-2-22-222-222-2-2-2200000000-222i−2i2i−2i−2i2i−2i2i000000000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ51222-2-222-2-2-2-22-222-222-2-2-2200000000-22−2i2i−2i2i2i−2i2i−2i0000000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ52222-2-222-2-2-2-22-222-222-2-2-2200000000-22−2i2i−2i2i2i−2i2i−2i000000000000-222-22i−2i−2i2i00000000000000000000000000000000
χ53222-2-222-2-2-2-22-222-2-2-2222-2000000002-22i−2i−2i2i−2i2i2i−2i000000000000000000002-2-22−2i2i2i−2i000000000000000000000000
χ54222-2-222-2-2-2-22-222-2-2-2222-2000000002-22i−2i−2i2i−2i2i2i−2i00000000000000000000-222-22i−2i−2i2i000000000000000000000000
χ55222-2-222-2-2-2-22-222-2-2-2222-2000000002-2−2i2i2i−2i2i−2i−2i2i000000000000000000002-2-222i−2i−2i2i000000000000000000000000
χ56222-2-222-2-2-2-22-222-2-2-2222-2000000002-2−2i2i2i−2i2i−2i−2i2i00000000000000000000-222-2−2i2i2i−2i000000000000000000000000
χ572-2-2-22222-2-2222-2-2-22-222-2-22i2i−2i−2i2i2i−2i−2i-220000000000002i−2i2i−2i000000000000000000002-22-22i−2i2i−2i0000000000000000
χ582-2-2-22222-2-2222-2-2-22-222-2-22i2i−2i−2i2i2i−2i−2i-220000000000002i−2i2i−2i00000000000000000000-22-22−2i2i−2i2i0000000000000000
χ592-2-2-22222-2-2222-2-2-22-222-2-2−2i−2i2i2i−2i−2i2i2i-22000000000000−2i2i−2i2i000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ602-2-2-22222-2-2222-2-2-22-222-2-2−2i−2i2i2i−2i−2i2i2i-22000000000000−2i2i−2i2i00000000000000000000-22-222i−2i2i−2i0000000000000000
χ612-2-2-22222-2-2222-2-2-2-22-2-2222i2i−2i−2i2i2i−2i−2i2-2000000000000−2i2i−2i2i00000000000000000000000000002-22-22i−2i2i−2i00000000
χ622-2-2-22222-2-2222-2-2-2-22-2-2222i2i−2i−2i2i2i−2i−2i2-2000000000000−2i2i−2i2i0000000000000000000000000000-22-22−2i2i−2i2i00000000
χ632-2-2-22222-2-2222-2-2-2-22-2-222−2i−2i2i2i−2i−2i2i2i2-20000000000002i−2i2i−2i00000000000000000000000000002-22-2−2i2i−2i2i00000000
χ642-2-2-22222-2-2222-2-2-2-22-2-222−2i−2i2i2i−2i−2i2i2i2-20000000000002i−2i2i−2i0000000000000000000000000000-22-222i−2i2i−2i00000000
χ652-2-2-2-2-22222-2-2222-22-22-22222-2-2-2-222-2-20000000000002-2-22000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ662-2-2-2-2-22222-2-2222-22-22-22222-2-2-2-222-2-20000000000002-2-2200000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ672-2-2-2-2-22222-2-2222-22-22-222-2-22222-2-2-2-2000000000000-222-2000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ682-2-2-2-2-22222-2-2222-22-22-222-2-22222-2-2-2-2000000000000-222-200000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ692-2-2-2-2-22222-2-2222-2-22-22-2-222-2-2-2-22222000000000000-222-200000000000000000000000000002-2-222-2-2200000000
χ702-2-2-2-2-22222-2-2222-2-22-22-2-222-2-2-2-22222000000000000-222-20000000000000000000000000000-222-2-222-200000000
χ712-2-2-2-2-22222-2-2222-2-22-22-2-2-2-22222-2-2220000000000002-2-2200000000000000000000000000002-2-22-222-200000000
χ722-2-2-2-2-22222-2-2222-2-22-22-2-2-2-22222-2-2220000000000002-2-220000000000000000000000000000-222-22-2-2200000000
χ7344-4444-444-4-4-4-44-4-40000004-44-44-44-400000000000000000000000000000000000000000000000000000000000000
χ7444-4444-444-4-4-4-44-4-4000000-44-44-44-4400000000000000000000000000000000000000000000000000000000000000
χ7544-44-4-4-44-4444-4-44-40000004i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7644-44-4-4-44-4444-4-44-4000000−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7744-4-44-4-4-44-4-444-444000000000000000000000000000000004-44-40000000000000000000000000000000000000000
χ7844-4-44-4-4-44-4-444-44400000000000000000000000000000000-44-440000000000000000000000000000000000000000
χ7944-4-4-44-4-4-444-444-44000000000000000000000000000000004-4-440000000000000000000000000000000000000000
χ8044-4-4-44-4-4-444-444-4400000000000000000000000000000000-444-40000000000000000000000000000000000000000
χ814-4444-4-4-4-44-4444-4-40000000000000000000000004i−4i4i−4i000000000000000000000000000000000000000000000000
χ824-4444-4-4-4-44-4444-4-4000000000000000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ834-444-44-4-44-44-44-44-40000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ844-444-44-4-44-44-44-44-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ854-44-444-44-44-4-4-4-4440000004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ864-44-444-44-44-4-4-4-444000000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ874-44-4-4-4-444-444-44-440000004-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ884-44-4-4-4-444-444-44-44000000-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
χ894-4-444-44-4-4-44-4-44444-4-44-44000000004-4000000000000000000000000000000000000000000000000000000000000
χ904-4-444-44-4-4-44-4-4444-444-44-400000000-44000000000000000000000000000000000000000000000000000000000000
χ914-4-44-444-444-44-4-4-444-4-4-44-40000000044000000000000000000000000000000000000000000000000000000000000
χ924-4-44-444-444-44-4-4-44-4444-4400000000-4-4000000000000000000000000000000000000000000000000000000000000

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