Finite Group Databasebeta

← Group #209792

Character table — Group #209792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444444444444444448888888888888888222244444444444444448888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-11111
χ91111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ17111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1ii−i−ii−i11-1-11-1iiii−i−i−i−i1111-1-1-1-11-11-11-1i−ii−iii−i−ii−i11-1-111-1-1ii−i−i1-1i−ii−i1-1
χ18111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1ii−i−ii−i11-1-11-1iiii−i−i−i−i1111-1-1-1-11-1-11-11i−i−ii−i−iii−ii-1-11111-1-1ii−i−i-11−ii−ii-11
χ19111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1ii−i−ii−i11-1-11-1−i−i−i−iiiii-1-1-1-111111-11-11-1i−ii−iii−i−ii−i11-1-1-1-111−i−iii-11−ii−ii-11
χ20111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1ii−i−ii−i11-1-11-1−i−i−i−iiiii-1-1-1-111111-1-11-11i−i−ii−i−iii−ii-1-111-1-111−i−iii1-1i−ii−i1-1
χ21111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1−i−iiii−i-1-1111-1iiii−i−i−i−i1111-1-1-1-1-111-11-1−iii−i−i−iiii−i-1-111-1-111−i−iii-11−iii−i1-1
χ22111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1−i−iiii−i-1-1111-1iiii−i−i−i−i1111-1-1-1-1-11-11-11−ii−iiii−i−i−ii11-1-1-1-111−i−iii1-1i−i−ii-11
χ23111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1−i−iiii−i-1-1111-1−i−i−i−iiiii-1-1-1-11111-111-11-1−iii−i−i−iiii−i-1-11111-1-1ii−i−i1-1i−i−ii-11
χ24111-1-1-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1−i−iiii−i-1-1111-1−i−i−i−iiiii-1-1-1-11111-11-11-11−ii−iiii−i−i−ii11-1-111-1-1ii−i−i-11−iii−i1-1
χ25111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1ii−i−i−ii-1-1111-1iiii−i−i−i−i-1-1-1-11111-111-11-1i−i−iiii−i−i−ii-1-11111-1-1−i−iii1-1−iii−i-11
χ26111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1ii−i−i−ii-1-1111-1iiii−i−i−i−i-1-1-1-11111-11-11-11i−ii−i−i−iiii−i11-1-111-1-1−i−iii-11i−i−ii1-1
χ27111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1ii−i−i−ii-1-1111-1−i−i−i−iiiii1111-1-1-1-1-111-11-1i−i−iiii−i−i−ii-1-111-1-111ii−i−i-11i−i−ii1-1
χ28111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1ii−i−i−ii-1-1111-1−i−i−i−iiiii1111-1-1-1-1-11-11-11i−ii−i−i−iiii−i11-1-1-1-111ii−i−i1-1−iii−i-11
χ29111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1−i−iii−ii11-1-11-1iiii−i−i−i−i-1-1-1-111111-11-11-1−ii−ii−i−iii−ii11-1-1-1-111ii−i−i-11i−ii−i-11
χ30111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1−i−iii−ii11-1-11-1iiii−i−i−i−i-1-1-1-111111-1-11-11−iii−iii−i−ii−i-1-111-1-111ii−i−i1-1−ii−ii1-1
χ31111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1−i−iii−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-11-11-11-1−ii−ii−i−iii−ii11-1-111-1-1−i−iii1-1−ii−ii1-1
χ32111-1-1-11-11-1−i−iii−i−iii1-1−i−iii1-11-1−i−iii−ii11-1-11-1−i−i−i−iiiii1111-1-1-1-11-1-11-11−iii−iii−i−ii−i-1-11111-1-1−i−iii-11i−ii−i-11
χ3322222222222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2-2-20000000000000000220000-2-20000000000000000000000000000
χ3422222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222-2-20000000000000000-2-20000220000000000000000000000000000
χ352222222222-2-2-2-22222-2-2222222-2-22222-2-22222-2-20000000000000000-2-20000-2-20000000000000000000000000000
χ362222222222-2-2-2-22222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000220000220000000000000000000000000000
χ3722222222-2-22222222222-2-2-2-2-2-2220000-2-20000-2-200000000000000000022-2-200-2-200002200000000000000000000
χ3822222222-2-22222222222-2-2-2-2-2-2220000-2-20000-2-2000000000000000000-2-22200220000-2-200000000000000000000
χ3922222222-2-22222-2-2-2-2-2-22222-2-2-2-20000-2-2000022000000000000000000000000002-22-2002-22-20000000000000000
χ4022222222-2-22222-2-2-2-2-2-22222-2-2-2-20000-2-200002200000000000000000000000000-22-2200-22-220000000000000000
χ4122222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000022000022000000000000000000000000002-22-200-22-220000000000000000
χ4222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200002200002200000000000000000000000000-22-22002-22-20000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2222222-2-2220000220000-2-200000000000000000022-2-200220000-2-200000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2222222-2-2220000220000-2-2000000000000000000-2-22200-2-200002200000000000000000000
χ45222-2-2-22-22-22i2i−2i−2i−2i−2i2i2i-22−2i−2i2i2i2-2-222i2i−2i−2i2i−2i-2-222-2200000000000000002-20000−2i2i0000000000000000000000000000
χ46222-2-2-22-22-22i2i−2i−2i−2i−2i2i2i-22−2i−2i2i2i2-2-22−2i−2i2i2i2i−2i22-2-2-220000000000000000-2200002i−2i0000000000000000000000000000
χ47222-2-2-22-22-2−2i−2i2i2i2i2i−2i−2i-222i2i−2i−2i2-2-222i2i−2i−2i−2i2i22-2-2-220000000000000000-220000−2i2i0000000000000000000000000000
χ48222-2-2-22-22-2−2i−2i2i2i2i2i−2i−2i-222i2i−2i−2i2-2-22−2i−2i2i2i−2i2i-2-222-2200000000000000002-200002i−2i0000000000000000000000000000
χ49222-2-2-22-2-222i2i−2i−2i2i2i−2i−2i2-2−2i−2i2i2i-222-20000−2i2i0000-220000000000000000002-2-2200−2i2i00002i−2i00000000000000000000
χ50222-2-2-22-2-222i2i−2i−2i2i2i−2i−2i2-2−2i−2i2i2i-222-20000−2i2i0000-22000000000000000000-222-2002i−2i0000−2i2i00000000000000000000
χ51222-2-2-22-2-222i2i−2i−2i−2i−2i2i2i-222i2i−2i−2i-22-220000−2i2i00002-2000000000000000000000000002i−2i−2i2i002-2-220000000000000000
χ52222-2-2-22-2-222i2i−2i−2i−2i−2i2i2i-222i2i−2i−2i-22-220000−2i2i00002-200000000000000000000000000−2i2i2i−2i00-222-20000000000000000
χ53222-2-2-22-2-22−2i−2i2i2i2i2i−2i−2i-22−2i−2i2i2i-22-2200002i−2i00002-2000000000000000000000000002i−2i−2i2i00-222-20000000000000000
χ54222-2-2-22-2-22−2i−2i2i2i2i2i−2i−2i-22−2i−2i2i2i-22-2200002i−2i00002-200000000000000000000000000−2i2i2i−2i002-2-220000000000000000
χ55222-2-2-22-2-22−2i−2i2i2i−2i−2i2i2i2-22i2i−2i−2i-222-200002i−2i0000-220000000000000000002-2-22002i−2i0000−2i2i00000000000000000000
χ56222-2-2-22-2-22−2i−2i2i2i−2i−2i2i2i2-22i2i−2i−2i-222-200002i−2i0000-22000000000000000000-222-200−2i2i00002i−2i00000000000000000000
χ572-2222-2-2-22-200002i−2i2i−2i002i−2i2i−2i-22002-22-2002i−2i2i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−2i2−i2i2−i200000000
χ582-2222-2-2-22-200002i−2i2i−2i002i−2i2i−2i-22002-22-2002i−2i2i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000−22−22−i2i2−i2i200000000
χ592-2222-2-2-22-200002i−2i2i−2i002i−2i2i−2i-2200-22-2200−2i2i−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000−22−22−i2i2−i2i200000000
χ602-2222-2-2-22-200002i−2i2i−2i002i−2i2i−2i-2200-22-2200−2i2i−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−2i2−i2i2−i200000000
χ612-2222-2-2-22-20000−2i2i−2i2i00−2i2i−2i2i-22002-22-200−2i2i−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−2−i2i2−i2i200000000
χ622-2222-2-2-22-20000−2i2i−2i2i00−2i2i−2i2i-22002-22-200−2i2i−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000−22−22i2−i2i2−i200000000
χ632-2222-2-2-22-20000−2i2i−2i2i00−2i2i−2i2i-2200-22-22002i−2i2i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000−22−22i2−i2i2−i200000000
χ642-2222-2-2-22-20000−2i2i−2i2i00−2i2i−2i2i-2200-22-22002i−2i2i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−2−i2i2−i2i200000000
χ652-22-2-22-222200002-2-22002-2-22-2-2002i−2i−2i2i00−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−222−2−2200000000
χ662-22-2-22-222200002-2-22002-2-22-2-2002i−2i−2i2i00−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−222−200000000
χ672-22-2-22-222200002-2-22002-2-22-2-200−2i2i2i−2i002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−222−200000000
χ682-22-2-22-222200002-2-22002-2-22-2-200−2i2i2i−2i002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−222−2−2200000000
χ692-22-2-22-22220000-222-200-222-2-2-2002i−2i−2i2i002i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−222−200000000
χ702-22-2-22-22220000-222-200-222-2-2-2002i−2i−2i2i002i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−22−2−2200000000
χ712-22-2-22-22220000-222-200-222-2-2-200−2i2i2i−2i00−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−22−2−2200000000
χ722-22-2-22-22220000-222-200-222-2-2-200−2i2i2i−2i00−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−222−200000000
χ7344-44-4-4-44004-44-4000000000000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ7444-44-4-4-44004-44-400000000000000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ7544-44-4-4-4400-44-44000000000000000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ7644-44-4-4-4400-44-4400000000000000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ7744-4-444-4-4004i−4i−4i4i000000000000000000000000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ7844-4-444-4-4004i−4i−4i4i00000000000000000000000000-22-222-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ7944-4-444-4-400−4i4i4i−4i000000000000000000000000002-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ8044-4-444-4-400−4i4i4i−4i00000000000000000000000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ814-4444-4-4-4-4400004i−4i4i−4i00−4i4i−4i4i4-4000000000000000000000000000000000000000000000000000000000000000000
χ824-4444-4-4-4-440000−4i4i−4i4i004i−4i4i−4i4-4000000000000000000000000000000000000000000000000000000000000000000
χ834-44-4-44-44-4-400004-4-4400-444-444000000000000000000000000000000000000000000000000000000000000000000
χ844-44-4-44-44-4-40000-444-4004-4-4444000000000000000000000000000000000000000000000000000000000000000000
χ854-4-44-444-4000000000044000000-4-40000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ864-4-44-444-4000000000044000000-4-4000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ874-4-44-444-40000000000-4-4000000440000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ884-4-44-444-40000000000-4-40000004400000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ894-4-4-44-44400000000004-4000000-4400000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ904-4-4-44-44400000000004-4000000-44000000000000−222222−2222−22−222200000000000000000000000000000000000000000000
χ914-4-4-44-4440000000000-440000004-40000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ924-4-4-44-4440000000000-440000004-400000000000000000000−222222−2222−22−2222000000000000000000000000000000000000

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