Finite Group Databasebeta

← Group #211432

Character table — Group #211432

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444448888888844448888888888884444444488888888888888888888888822224444
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
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1711-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-11-11-1i−ii−i
χ1811-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-111-1-1ii−i−i-1-111−i−iii−i−iii-1-111ii−i−i11-1-1-11-11−ii−ii
χ1911-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1-1-111−i−iii11-1-1ii−i−iii−i−i11-1-1−i−iii-1-111-11-11−ii−ii
χ2011-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1iiii−i−i−i−i1-1i−i11-1-1ii−i−i11-1-1-1-111−i−iii-1-111−i−iii−i−iii-1-111−i−iii-1-1111-11-1i−ii−i
χ2111-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiii1-1i−i-1-111−i−iii-1-11111-1-1ii−i−i11-1-1ii−i−i−i−iii-1-111−i−iii-1-1111-1-11i−i−ii
χ2211-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiii1-1i−i-1-111−i−iii-1-11111-1-1ii−i−i-1-111−i−iiiii−i−i11-1-1−i−iii-1-111-111-1−iii−i
χ2311-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiii1-1i−i-1-111−i−iii-1-111-1-111−i−iii11-1-1ii−i−i−i−iii-1-111ii−i−i11-1-1-111-1−iii−i
χ2411-111-1-1-1ii−i−iii−i−iii−i−i1-111-1-11-1−i−i−i−iiiii1-1i−i-1-111−i−iii-1-111-1-111−i−iii-1-111−i−iiiii−i−i11-1-1ii−i−i11-1-11-1-11i−i−ii
χ2511-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i1-1−ii-1-111ii−i−i-1-11111-1-1−i−iii11-1-1−i−iiiii−i−i-1-111ii−i−i-1-1111-1-11−iii−i
χ2611-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i1-1−ii-1-111ii−i−i-1-11111-1-1−i−iii-1-111ii−i−i−i−iii11-1-1ii−i−i-1-111-111-1i−i−ii
χ2711-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i1-1−ii-1-111ii−i−i-1-111-1-111ii−i−i11-1-1−i−iiiii−i−i-1-111−i−iii11-1-1-111-1i−i−ii
χ2811-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1iiii−i−i−i−i1-1−ii-1-111ii−i−i-1-111-1-111ii−i−i-1-111ii−i−i−i−iii11-1-1−i−iii11-1-11-1-11−iii−i
χ2911-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-111-1-1−i−iii11-1-1−i−iii−i−iii11-1-1−i−iii11-1-11-11-1−ii−ii
χ3011-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-111-1-1−i−iii-1-111ii−i−iii−i−i-1-111−i−iii11-1-1-11-11i−ii−i
χ3111-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1-1-111ii−i−i11-1-1−i−iii−i−iii11-1-1ii−i−i-1-111-11-11i−ii−i
χ3211-111-1-1-1−i−iii−i−iii−i−iii1-111-1-11-1−i−i−i−iiiii1-1−ii11-1-1−i−iii11-1-1-1-111ii−i−i-1-111ii−i−iii−i−i-1-111ii−i−i-1-1111-11-1−ii−ii
χ332222222222222222-2-2-2-2-2-22222-2-200000000-2-2-2-20000000000002-22-22-22-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-22222-2-200000000-2-2-2-2000000000000-22-22-22-2200000000000000000000000000000000
χ35222222222222-2-2-2-2222222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ36222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ3922222222-2-2-2-222222222-2-2-2-2-2-2-2-20000000022-2-20000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000
χ4022222222-2-2-2-222222222-2-2-2-2-2-2-2-20000000022-2-2000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ4122222222-2-2-2-22222-2-2-2-222-2-2-2-22222222222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ4222222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-22222-2-200000000-2-2220000000000002-22-2-22-2200000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-22222-2-200000000-2-222000000000000-22-222-22-200000000000000000000000000000000
χ45222-2-2-2-222-22-200002-22-2220000-2-222-2-222-2-200002-22-20000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ46222-2-2-2-222-22-200002-22-2220000-2-222-2-222-2-200002-22-20000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ47222-2-2-2-222-22-200002-22-2220000-2-2-2-222-2-2220000-22-220000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ48222-2-2-2-222-22-200002-22-2220000-2-2-2-222-2-2220000-22-220000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ49222-2-2-2-22-22-220000-22-22220000-2-222-2-222-2-20000-22-220000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ50222-2-2-2-22-22-220000-22-22220000-2-222-2-222-2-20000-22-220000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ51222-2-2-2-22-22-220000-22-22220000-2-2-2-222-2-22200002-22-20000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ52222-2-2-2-22-22-220000-22-22220000-2-2-2-222-2-22200002-22-20000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ5322-222-2-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-2222-2-2-2200000000-22−2i2i0000000000002-2-222i−2i−2i2i00000000000000000000000000000000
χ5422-222-2-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-2222-2-2-2200000000-22−2i2i000000000000-222-2−2i2i2i−2i00000000000000000000000000000000
χ5522-222-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-2-2-2222-22i2i2i2i−2i−2i−2i−2i-22−2i2i22-2-2−2i−2i2i2i-2-2220000000000000000000000000000000000000000
χ5622-222-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2-2-2-2222-2−2i−2i−2i−2i2i2i2i2i-22−2i2i-2-2222i2i−2i−2i22-2-20000000000000000000000000000000000000000
χ5722-222-2-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-22-2-222-22000000002-22i−2i0000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ5822-222-2-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-22-2-222-22000000002-22i−2i000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ5922-222-2-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-22-2-222-22000000002-2−2i2i0000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ6022-222-2-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-22-2-222-22000000002-2−2i2i000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ6122-222-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-2-2-2222-22i2i2i2i−2i−2i−2i−2i-222i−2i-2-222−2i−2i2i2i22-2-20000000000000000000000000000000000000000
χ6222-222-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2-2-2-2222-2−2i−2i−2i−2i2i2i2i2i-222i−2i22-2-22i2i−2i−2i-2-2220000000000000000000000000000000000000000
χ6322-222-2-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-2222-2-2-2200000000-222i−2i0000000000002-2-22−2i2i2i−2i00000000000000000000000000000000
χ6422-222-2-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-2222-2-2-2200000000-222i−2i000000000000-222-22i−2i−2i2i00000000000000000000000000000000
χ6522-2-2-222-22i−2i−2i2i00002i−2i−2i2i2-20000-222i2i−2i−2i−2i−2i2i2i00002-2-220000000000000000i2−i2−i2i2−222−2−222−2i2−i2−i2i20000000000000000
χ6622-2-2-222-22i−2i−2i2i00002i−2i−2i2i2-20000-222i2i−2i−2i−2i−2i2i2i00002-2-220000000000000000−i2i2i2−i22−2−222−2−22−i2i2i2−i20000000000000000
χ6722-2-2-222-22i−2i−2i2i00002i−2i−2i2i2-20000-22−2i−2i2i2i2i2i−2i−2i0000-222-20000000000000000i2−i2−i2i2−222−22−2−22−i2i2i2−i20000000000000000
χ6822-2-2-222-22i−2i−2i2i00002i−2i−2i2i2-20000-22−2i−2i2i2i2i2i−2i−2i0000-222-20000000000000000−i2i2i2−i22−2−22−222−2i2−i2−i2i20000000000000000
χ6922-2-2-222-2−2i2i2i−2i0000−2i2i2i−2i2-20000-222i2i−2i−2i−2i−2i2i2i0000-222-20000000000000000i2−i2−i2i22−2−22−222−2−i2i2i2−i20000000000000000
χ7022-2-2-222-2−2i2i2i−2i0000−2i2i2i−2i2-20000-222i2i−2i−2i−2i−2i2i2i0000-222-20000000000000000−i2i2i2−i2−222−22−2−22i2−i2−i2i20000000000000000
χ7122-2-2-222-2−2i2i2i−2i0000−2i2i2i−2i2-20000-22−2i−2i2i2i2i2i−2i−2i00002-2-220000000000000000i2−i2−i2i22−2−222−2−22i2−i2−i2i20000000000000000
χ7222-2-2-222-2−2i2i2i−2i0000−2i2i2i−2i2-20000-22−2i−2i2i2i2i2i−2i−2i00002-2-220000000000000000−i2i2i2−i2−222−2−222−2−i2i2i2−i20000000000000000
χ73444-4-4-4-444-44-40000-44-44-4-40000440000000000000000000000000000000000000000000000000000000000000000
χ74444-4-4-4-44-44-4400004-44-4-4-40000440000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-44i−4i−4i4i0000−4i4i4i−4i-4400004-40000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4−4i4i4i−4i00004i−4i−4i4i-4400004-40000000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-4000000000000004-44-4002i2−2i22i2−2i22i2−2i22i2−2i2000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ784-444-44-4-4000000000000004-44-400−2i22i2−2i22i2−2i22i2−2i22i200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ794-444-44-4-400000000000000-44-44002i2−2i22i2−2i22i2−2i22i2−2i200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ804-444-44-4-400000000000000-44-4400−2i22i2−2i22i2−2i22i2−2i22i2000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ814-44-44-44-400004i−4i4i−4i0000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000022−2222−220000000000000000000000000000000000000000
χ824-44-44-44-400004i−4i4i−4i000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000−2222−22220000000000000000000000000000000000000000
χ834-44-44-44-40000−4i4i−4i4i0000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000−2222−22220000000000000000000000000000000000000000
χ844-44-44-44-40000−4i4i−4i4i000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000022−2222−220000000000000000000000000000000000000000
χ854-4-44-4-444000000000000004-4-440022−2222−22−2222−22220000000022−22−222200000000000000000000000000000000000000000000
χ864-4-44-4-444000000000000004-4-4400−2222−222222−2222−2200000000−222222−2200000000000000000000000000000000000000000000
χ874-4-44-4-44400000000000000-444-40022−2222−22−2222−222200000000−222222−2200000000000000000000000000000000000000000000
χ884-4-44-4-44400000000000000-444-400−2222−222222−2222−220000000022−22−222200000000000000000000000000000000000000000000
χ894-4-4-444-4400004-4-4400000000000022−22−2222−222222−2200000000000022−22−22220000000000000000000000000000000000000000
χ904-4-4-444-4400004-4-44000000000000−222222−2222−22−2222000000000000−222222−220000000000000000000000000000000000000000
χ914-4-4-444-440000-444-400000000000022−22−2222−222222−22000000000000−222222−220000000000000000000000000000000000000000
χ924-4-4-444-440000-444-4000000000000−222222−2222−22−222200000000000022−22−22220000000000000000000000000000000000000000

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