Finite Group Databasebeta

← Group #209752

Character table — Group #209752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444444444444444448888888888888888224444444444444444448888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111
χ91111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-111
χ121111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ1711-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−iii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-11-1i−i1-11-1ii−i−i11-1-1i−ii−i11-1-1ii−i−i1-1i−ii−i1-1
χ1811-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−iii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1-11−ii1-1-11−i−iii-1-111i−i−ii11-1-1ii−i−i-11−ii−ii-11
χ1911-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−iii−i−i11-1-11-1−i−i−i−iiiii-1-1-1-111111-1i−i1-11-1ii−i−i11-1-1i−ii−i-1-111−i−iii-11−ii−ii-11
χ2011-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−iii−i−i11-1-11-1−i−i−i−iiiii-1-1-1-11111-11−ii1-1-11−i−iii-1-111i−i−ii-1-111−i−iii1-1i−ii−i1-1
χ2111-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−i−i−iii-1-1111-1iiii−i−i−i−i1111-1-1-1-11-1i−i-111-1−i−iii-1-111−iii−i-1-111−i−iii-11−iii−i1-1
χ2211-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−i−i−iii-1-1111-1iiii−i−i−i−i1111-1-1-1-1-11−ii-11-11ii−i−i11-1-1−ii−ii-1-111−i−iii1-1i−i−ii-11
χ2311-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−i−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-111111-1i−i-111-1−i−iii-1-111−iii−i11-1-1ii−i−i1-1i−i−ii-11
χ2411-1-11-11-11-1ii−i−i1-1ii−i−iii−i−i1-11-1i−i−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111-11−ii-11-11ii−i−i11-1-1−ii−ii11-1-1ii−i−i-11−iii−i1-1
χ2511-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−iiii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-111111-1−ii-111-1ii−i−i-1-111i−i−ii11-1-1−i−iii1-1−iii−i-11
χ2611-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−iiii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111-11i−i-11-11−i−iii11-1-1i−ii−i11-1-1−i−iii-11i−i−ii1-1
χ2711-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−iiii−i−i-1-1111-1−i−i−i−iiiii1111-1-1-1-11-1−ii-111-1ii−i−i-1-111i−i−ii-1-111ii−i−i-11i−i−ii1-1
χ2811-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−iiii−i−i-1-1111-1−i−i−i−iiiii1111-1-1-1-1-11i−i-11-11−i−iii11-1-1i−ii−i-1-111ii−i−i1-1−iii−i-11
χ2911-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−ii−i−iii11-1-11-1iiii−i−i−i−i-1-1-1-111111-1−ii1-11-1−i−iii11-1-1−ii−ii-1-111ii−i−i-11i−ii−i-11
χ3011-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−ii−i−iii11-1-11-1iiii−i−i−i−i-1-1-1-11111-11i−i1-1-11ii−i−i-1-111−iii−i-1-111ii−i−i1-1−ii−ii1-1
χ3111-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−ii−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-11-1−ii1-11-1−i−iii11-1-1−ii−ii11-1-1−i−iii1-1−ii−ii1-1
χ3211-1-11-11-11-1−i−iii1-1−i−iii−i−iii1-11-1−ii−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1-11i−i1-1-11ii−i−i-1-111−iii−i11-1-1−i−iii-11i−ii−i-11
χ3322222222222222-2-22222-2-2-2-222-2-2-2-200000000-2-2000000000000000022-2-200-2-20000000000220000000000000000
χ3422222222222222-2-22222-2-2-2-222-2-2-2-200000000-2-20000000000000000-2-22200220000000000-2-20000000000000000
χ352222222222-2-2-2-2-2-2-2-2-2-2222222-2-22200000000-2-20000000000000000222200-2-20000000000-2-20000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2222222-2-22200000000-2-20000000000000000-2-2-2-200220000000000220000000000000000
χ3722222222-2-2222222-2-2-2-22222-2-222-2-222222222-2-200000000000000000000-2-20000000000-2-2000000000000000000
χ3822222222-2-2222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000022000000000022000000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-22200000000220000000000000000000000002-22-22-22-200000000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000000022000000000000000000000000-22-22-22-2200000000000000000000
χ4122222222-2-2-2-2-2-2222222-2-2-2-2-2-222222222-2-2-2-2-2-200000000000000000000220000000000-2-2000000000000000000
χ4222222222-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-22222-2-200000000000000000000-2-2000000000022000000000000000000
χ4322222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-200000000220000000000000000000000002-22-2-22-2200000000000000000000
χ4422222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-20000000022000000000000000000000000-22-222-22-200000000000000000000
χ4522-2-22-22-22-22i2i−2i−2i-222i2i−2i−2i−2i−2i2i2i2-2-22−2i2i00000000-2200000000000000002-2−2i2i00-2200000000002i−2i0000000000000000
χ4622-2-22-22-22-22i2i−2i−2i-222i2i−2i−2i−2i−2i2i2i2-2-22−2i2i00000000-220000000000000000-222i−2i002-20000000000−2i2i0000000000000000
χ4722-2-22-22-22-2−2i−2i2i2i-22−2i−2i2i2i2i2i−2i−2i2-2-222i−2i00000000-2200000000000000002-22i−2i00-220000000000−2i2i0000000000000000
χ4822-2-22-22-22-2−2i−2i2i2i-22−2i−2i2i2i2i2i−2i−2i2-2-222i−2i00000000-220000000000000000-22−2i2i002-200000000002i−2i0000000000000000
χ4922-2-22-22-2-222i2i−2i−2i2-2−2i−2i2i2i2i2i−2i−2i-222-2−2i2i2i2i−2i−2i22-2-2-2200000000000000000000-220000000000−2i2i000000000000000000
χ5022-2-22-22-2-222i2i−2i−2i2-2−2i−2i2i2i2i2i−2i−2i-222-2−2i2i−2i−2i2i2i-2-222-22000000000000000000002-200000000002i−2i000000000000000000
χ5122-2-22-22-2-222i2i−2i−2i-22−2i−2i2i2i−2i−2i2i2i-22-222i−2i000000002-20000000000000000000000002i−2i−2i2i2-2-2200000000000000000000
χ5222-2-22-22-2-222i2i−2i−2i-22−2i−2i2i2i−2i−2i2i2i-22-222i−2i000000002-2000000000000000000000000−2i2i2i−2i-222-200000000000000000000
χ5322-2-22-22-2-22−2i−2i2i2i2-22i2i−2i−2i−2i−2i2i2i-222-22i−2i2i2i−2i−2i-2-222-22000000000000000000002-20000000000−2i2i000000000000000000
χ5422-2-22-22-2-22−2i−2i2i2i2-22i2i−2i−2i−2i−2i2i2i-222-22i−2i−2i−2i2i2i22-2-2-2200000000000000000000-2200000000002i−2i000000000000000000
χ5522-2-22-22-2-22−2i−2i2i2i-222i2i−2i−2i2i2i−2i−2i-22-22−2i2i000000002-20000000000000000000000002i−2i−2i2i-222-200000000000000000000
χ5622-2-22-22-2-22−2i−2i2i2i-222i2i−2i−2i2i2i−2i−2i-22-22−2i2i000000002-2000000000000000000000000−2i2i2i−2i2-2-2200000000000000000000
χ572-22-222-2-2002i−2i2i−2i2-200002i−2i2i−2i00-22002-22-22i−2i2i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−2i2−i2i2−i200000000
χ582-22-222-2-2002i−2i2i−2i2-200002i−2i2i−2i00-22002-22-22i−2i2i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000000−22−22−i2i2−i2i200000000
χ592-22-222-2-2002i−2i2i−2i2-200002i−2i2i−2i00-2200-22-22−2i2i−2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000000−22−22−i2i2−i2i200000000
χ602-22-222-2-2002i−2i2i−2i2-200002i−2i2i−2i00-2200-22-22−2i2i−2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−2i2−i2i2−i200000000
χ612-22-222-2-200−2i2i−2i2i2-20000−2i2i−2i2i00-22002-22-2−2i2i−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000000000002−22−2−i2i2−i2i200000000
χ622-22-222-2-200−2i2i−2i2i2-20000−2i2i−2i2i00-22002-22-2−2i2i−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000000−22−22i2−i2i2−i200000000
χ632-22-222-2-200−2i2i−2i2i2-20000−2i2i−2i2i00-2200-22-222i−2i2i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000000−22−22i2−i2i2−i200000000
χ642-22-222-2-200−2i2i−2i2i2-20000−2i2i−2i2i00-2200-22-222i−2i2i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000000000002−22−2−i2i2−i2i200000000
χ652-2-222-2-22002-2-222200002-2-2200-2-2002i−2i−2i2i−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−222−2−2200000000
χ662-2-222-2-22002-2-222200002-2-2200-2-2002i−2i−2i2i−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−222−200000000
χ672-2-222-2-22002-2-222200002-2-2200-2-200−2i2i2i−2i2i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−222−200000000
χ682-2-222-2-22002-2-222200002-2-2200-2-200−2i2i2i−2i2i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−222−2−2200000000
χ692-2-222-2-2200-222-2220000-222-200-2-2002i−2i−2i2i2i−2i−2i2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−222−200000000
χ702-2-222-2-2200-222-2220000-222-200-2-2002i−2i−2i2i2i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−22−2−2200000000
χ712-2-222-2-2200-222-2220000-222-200-2-200−2i2i2i−2i−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−22−2−2200000000
χ722-2-222-2-2200-222-2220000-222-200-2-200−2i2i2i−2i−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−222−200000000
χ73444-4-4-4-444-400000000000000-44000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ74444-4-4-4-444-400000000000000-4400000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ75444-4-4-4-44-44000000000000004-400000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ76444-4-4-4-44-44000000000000004-40000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ7744-44-44-4-44400000000000000-4-40000000000000022−2222−22−2222−222200000000000000000000000000000000000000000000
χ7844-44-44-4-44400000000000000-4-400000000000000−2222−222222−2222−2200000000000000000000000000000000000000000000
χ7944-44-44-4-4-4-4000000000000004400000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ8044-44-44-4-4-4-400000000000000440000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ814-444-4-44-4000000004i−4i4i−4i000000000000000000002i−2i−2i2i2i−2i−2i2i2-2-222-2-22000000000000000000000000000000000000
χ824-444-4-44-4000000004i−4i4i−4i00000000000000000000−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000000000
χ834-444-4-44-400000000−4i4i−4i4i000000000000000000002i−2i−2i2i2i−2i−2i2i-222-2-222-2000000000000000000000000000000000000
χ844-444-4-44-400000000−4i4i−4i4i00000000000000000000−2i2i2i−2i−2i2i2i−2i2-2-222-2-22000000000000000000000000000000000000
χ854-44-444-4-4004i−4i4i−4i-440000−4i4i−4i4i004-40000000000000000000000000000000000000000000000000000000000000000
χ864-44-444-4-400−4i4i−4i4i-4400004i−4i4i−4i004-40000000000000000000000000000000000000000000000000000000000000000
χ874-4-444-4-44004-4-44-4-40000-444-400440000000000000000000000000000000000000000000000000000000000000000
χ884-4-444-4-4400-444-4-4-400004-4-4400440000000000000000000000000000000000000000000000000000000000000000
χ894-4-4-4-4444000000004-4-44000000000000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ904-4-4-4-4444000000004-4-4400000000000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ914-4-4-4-444400000000-444-4000000000000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000000000
χ924-4-4-4-444400000000-444-400000000000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000000000

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