Finite Group Databasebeta

← Group #384147

Character table — Group #384147

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222224444444444444444444444448888888888888888222244444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-11111-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ171111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−i11-1-111-1-1ii−i−ii−ii−i1-1i−i
χ181111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1111-1i−i-1-111−i−iii-1-11111-1-1ii−i−i−ii−ii-11−ii
χ191111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii11-1-11-1i−i11-1-1−i−iii-1-111-1-111−i−iiii−ii−i-11−ii
χ201111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii-1-1111-1i−i-1-111ii−i−i11-1-1-1-111−i−iii−ii−ii1-1i−i
χ211111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i11-1-1-11−ii-1-111ii−i−i-1-111-1-111−i−iiii−i−ii1-1−ii
χ221111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i-1-111-11−ii11-1-1−i−iii11-1-1-1-111−i−iii−iii−i-11i−i
χ231111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1-11−ii-1-111−i−iii11-1-111-1-1ii−i−ii−i−ii-11i−i
χ241111-1-11-1-11-1-111-1-111-1-1-111-1iiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111-11−ii11-1-1ii−i−i-1-11111-1-1ii−i−i−iii−i1-1−ii
χ251111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii11-1-111-1-1−i−iii−ii−ii1-1−ii
χ261111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1111-1−ii-1-111ii−i−i-1-11111-1-1−i−iiii−ii−i-11i−i
χ271111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i11-1-11-1−ii11-1-1ii−i−i-1-111-1-111ii−i−i−ii−ii-11i−i
χ281111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-1111-1−ii-1-111−i−iii11-1-1-1-111ii−i−ii−ii−i1-1−ii
χ291111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii11-1-1-11i−i-1-111−i−iii-1-111-1-111ii−i−i−iii−i1-1i−i
χ301111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii-1-111-11i−i11-1-1ii−i−i11-1-1-1-111ii−i−ii−i−ii-11−ii
χ311111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1-11i−i-1-111ii−i−i11-1-111-1-1−i−iii−iii−i-11−ii
χ321111-1-11-1-11-1-111-1-111-1-1-111-1−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-111-11i−i11-1-1−i−iii-1-11111-1-1−i−iiii−i−ii1-1i−i
χ332222222222222222-2-2-2-2-2-2-2-222-2-222-2-22222222200000000000000000000-2-2-2-20000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-20000000000000000000022220000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-200000000000000000000-2-2220000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-222220000000000000000000022-2-20000000000000000000000000000
χ372222-2-22-2-22-2-222-2-2-2-2222-2-222i2i−2i−2i−2i−2i2i2i22-2-22i2i−2i−2i00000000000000000000-22−2i2i0000000000000000000000000000
χ382222-2-22-2-22-2-222-2-2-2-2222-2-222i2i−2i−2i−2i−2i2i2i-2-222−2i−2i2i2i000000000000000000002-22i−2i0000000000000000000000000000
χ392222-2-22-2-22-2-222-2-2-2-2222-2-22−2i−2i2i2i2i2i−2i−2i22-2-2−2i−2i2i2i00000000000000000000-222i−2i0000000000000000000000000000
χ402222-2-22-2-22-2-222-2-2-2-2222-2-22−2i−2i2i2i2i2i−2i−2i-2-2222i2i−2i−2i000000000000000000002-2−2i2i0000000000000000000000000000
χ41222-222-2-2-2-2222-2-2-22-22-2-22-2200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i00002-22-20000000000000000
χ42222-222-2-2-2-2222-2-2-22-22-2-22-2200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i0000-22-220000000000000000
χ43222-222-2-2-2-2222-2-2-22-22-2-22-220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i0000-22-220000000000000000
χ44222-222-2-2-2-2222-2-2-22-22-2-22-220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i00002-22-20000000000000000
χ45222-2-2-2-222-2-2-22-2222-2-2222-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i00002-2-220000000000000000
χ46222-2-2-2-222-2-2-22-2222-2-2222-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i0000-222-20000000000000000
χ47222-2-2-2-222-2-2-22-2222-2-2222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i0000-222-20000000000000000
χ48222-2-2-2-222-2-2-22-2222-2-2222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i00002-2-220000000000000000
χ4922-2-22-222-222-2-2-22-2000000002-2002-2002i−2i2i−2i2i−2i2i−2i2−22−22−22−222−2−222−2−200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ5022-2-22-222-222-2-2-22-2000000002-2002-2002i−2i2i−2i2i−2i2i−2i−22−22−22−22−2−222−2−22200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ5122-2-22-222-222-2-2-22-2000000002-2002-200−2i2i−2i2i−2i2i−2i2i2−22−22−22−222−2−222−2−200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ5222-2-22-222-222-2-2-22-2000000002-2002-200−2i2i−2i2i−2i2i−2i2i−22−22−22−22−2−222−2−22200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ5322-2-22-222-222-2-2-22-200000000-2200-22002i−2i2i−2i−2i2i−2i2i2−22−22−22−2−2−222−2−22200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ5422-2-22-222-222-2-2-22-200000000-2200-22002i−2i2i−2i−2i2i−2i2i−22−22−22−2222−2−222−2−200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ5522-2-22-222-222-2-2-22-200000000-2200-2200−2i2i−2i2i2i−2i2i−2i2−22−22−22−2−2−222−2−22200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ5622-2-22-222-222-2-2-22-200000000-2200-2200−2i2i−2i2i2i−2i2i−2i−22−22−22−2222−2−222−2−200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ5722-2-2-222-222-22-2-2-22000000002i−2i00−2i2i002i−2i−2i2i-222-22−22−2−22−22i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2−222−200000000
χ5822-2-2-222-222-22-2-2-22000000002i−2i00−2i2i002i−2i−2i2i-222-2−22−222−22−2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i22−2−2200000000
χ5922-2-2-222-222-22-2-2-22000000002i−2i00−2i2i00−2i2i2i−2i2-2-222−22−2−22−22i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i22−2−2200000000
χ6022-2-2-222-222-22-2-2-22000000002i−2i00−2i2i00−2i2i2i−2i2-2-22−22−222−22−2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2−222−200000000
χ6122-2-2-222-222-22-2-2-2200000000−2i2i002i−2i002i−2i−2i2i2-2-222−22−2−22−22−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i22−2−2200000000
χ6222-2-2-222-222-22-2-2-2200000000−2i2i002i−2i002i−2i−2i2i2-2-22−22−222−22−2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2−222−200000000
χ6322-2-2-222-222-22-2-2-2200000000−2i2i002i−2i00−2i2i2i−2i-222-22−22−2−22−22−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2−222−200000000
χ6422-2-2-222-222-22-2-2-2200000000−2i2i002i−2i00−2i2i2i−2i-222-2−22−222−22−2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i22−2−2200000000
χ652-2-2-22-22-2-2-2-222222-22-22-22-220000000000000000000000002-22-22-22-22-22-2000000002-22-200000000000000000000
χ662-2-2-22-22-2-2-2-222222-22-22-22-220000000000000000000000002-22-22-22-2-22-2200000000-22-2200000000000000000000
χ672-2-2-22-22-2-2-2-222222-22-22-22-22000000000000000000000000-22-22-22-222-22-200000000-22-2200000000000000000000
χ682-2-2-22-22-2-2-2-222222-22-22-22-22000000000000000000000000-22-22-22-22-22-22000000002-22-200000000000000000000
χ692-2-2-2-22222-22-222-2-2-222-222-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i2-2-22000000002i−2i−2i2i00000000000000000000
χ702-2-2-2-22222-22-222-2-2-222-222-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i-222-200000000−2i2i2i−2i00000000000000000000
χ712-2-2-2-22222-22-222-2-2-222-222-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i2-2-2200000000−2i2i2i−2i00000000000000000000
χ722-2-2-2-22222-22-222-2-2-222-222-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i-222-2000000002i−2i−2i2i00000000000000000000
χ73444-444-4-4-4-4444-4-4-4-44-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-444-4-4-44-444-444-4-4-44400000000000000000000000000000000000000000000000000000000000000000000
χ7544-444-4-4-44-44-4-44-440000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ7644-444-4-4-44-44-4-44-44000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7744-44-44-44-4-4-44-444-40000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7844-44-44-44-4-4-44-444-4000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ794-444444-44-4-4-4-4-44-40000000000000000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ804-444444-44-4-4-4-4-44-400000000000000000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ814-444-4-444-4-444-4-4-44000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ824-444-4-444-4-444-4-4-4400000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ834-44-444-44-44-4-4-44-4400000000004i−4i004i−4i000000000000000000000000000000000000000000000000000000000000
χ844-44-444-44-44-4-4-44-440000000000−4i4i00−4i4i000000000000000000000000000000000000000000000000000000000000
χ854-44-4-4-4-4-44444-444-400000000004-400-44000000000000000000000000000000000000000000000000000000000000
χ864-44-4-4-4-4-44444-444-40000000000-44004-4000000000000000000000000000000000000000000000000000000000000
χ874-4-444-4-4444-444-4-4-44444-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ884-4-444-4-4444-444-4-4-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000000000
χ894-4-44-44-4-4-444-44-44444-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ904-4-44-44-4-4-444-44-444-4-444-444-400000000000000000000000000000000000000000000000000000000000000000000
χ914-4-4-44-44-4-4-4-4444444-44-44-44-400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-44444-44-444-4-44-4-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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