Finite Group Databasebeta

← Group #209783

Character table — Group #209783

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444442222444444448888888888888888444444444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111
χ91111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1711-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-111-1-1ii−i−ii−i1-1iiii−i−i−i−i1111-1-1-1-11-1i−ii−ii−iii−i−i1-11-111-1-1ii−i−i11-1-1i−i1-1i−i1-1
χ1811-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-111-1-1ii−i−ii−i1-1iiii−i−i−i−i1111-1-1-1-1-11i−i−ii−ii−i−iii1-1-11-1-111ii−i−i11-1-1−ii-11−ii-11
χ1911-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-111-1-1ii−i−ii−i1-1−i−i−i−iiiii-1-1-1-111111-1i−ii−ii−iii−i−i1-11-111-1-1−i−iii-1-111−ii-11−ii-11
χ2011-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-111-1-1ii−i−ii−i1-1−i−i−i−iiiii-1-1-1-11111-11i−i−ii−ii−i−iii1-1-11-1-111−i−iii-1-111i−i1-1i−i1-1
χ2111-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-1-1-111−i−iiii−i1-1iiii−i−i−i−i1111-1-1-1-11-1−iii−ii−i−i−iii-111-1-1-111−i−iii-1-111−ii-11i−i1-1
χ2211-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-1-1-111−i−iiii−i1-1iiii−i−i−i−i1111-1-1-1-1-11−ii−ii−iiii−i−i-11-1111-1-1−i−iii-1-111i−i1-1−ii-11
χ2311-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-1-1-111−i−iiii−i1-1−i−i−i−iiiii-1-1-1-111111-1−iii−ii−i−i−iii-111-1-1-111ii−i−i11-1-1i−i1-1−ii-11
χ2411-11-1-1-111-1ii−i−iii−i−iii−i−i1-11-11-1-1-111−i−iiii−i1-1−i−i−i−iiiii-1-1-1-11111-11−ii−ii−iiii−i−i-11-1111-1-1ii−i−i11-1-1−ii-11i−i1-1
χ2511-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-111-1-1−i−iii−ii1-1iiii−i−i−i−i-1-1-1-111111-1−ii−ii−ii−i−iii1-11-111-1-1ii−i−i-1-111i−i-11i−i-11
χ2611-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-111-1-1−i−iii−ii1-1iiii−i−i−i−i-1-1-1-11111-11−iii−ii−iii−i−i1-1-11-1-111ii−i−i-1-111−ii1-1−ii1-1
χ2711-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-111-1-1−i−iii−ii1-1−i−i−i−iiiii1111-1-1-1-11-1−ii−ii−ii−i−iii1-11-111-1-1−i−iii11-1-1−ii1-1−ii1-1
χ2811-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-111-1-1−i−iii−ii1-1−i−i−i−iiiii1111-1-1-1-1-11−iii−ii−iii−i−i1-1-11-1-111−i−iii11-1-1i−i-11i−i-11
χ2911-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-1-1-111ii−i−i−ii1-1iiii−i−i−i−i-1-1-1-111111-1i−i−ii−iiii−i−i-111-1-1-111−i−iii11-1-1−ii1-1i−i-11
χ3011-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-1-1-111ii−i−i−ii1-1iiii−i−i−i−i-1-1-1-11111-11i−ii−ii−i−i−iii-11-1111-1-1−i−iii11-1-1i−i-11−ii1-1
χ3111-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-1-1-111ii−i−i−ii1-1−i−i−i−iiiii1111-1-1-1-11-1i−i−ii−iiii−i−i-111-1-1-111ii−i−i-1-111i−i-11−ii1-1
χ3211-11-1-1-111-1−i−iii−i−iii−i−iii1-11-11-1-1-111ii−i−i−ii1-1−i−i−i−iiiii1111-1-1-1-1-11i−ii−ii−i−i−iii-11-1111-1-1ii−i−i-1-111−ii1-1i−i-11
χ33222222222222222222-2-2-2-2-2-222-2-222222222-2-2-2-2000000000000000000-2-200000000-2-20000000000000000000000
χ34222222222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000002200000000220000000000000000000000
χ352222222222-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2-2-222-2-20000000000000000002200000000-2-20000000000000000000000
χ362222222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-2222222-2-2000000000000000000-2-200000000220000000000000000000000
χ3722222222-2-22222-2-2-2-22222-2-2-2-2-2-200000000-2-2220000000000000000000000002-22-200002-22-20000000000000000
χ3822222222-2-22222-2-2-2-22222-2-2-2-2-2-200000000-2-222000000000000000000000000-22-220000-22-220000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-222-2-2220000000022-2-200000000000000002200-2-222000000-2-200000000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-222-2-2220000000022-2-20000000000000000-2-20022-2-20000002200000000000000000000
χ4122222222-2-2-2-2-2-22222222222-2-22200000000-2-2-2-20000000000000000220022-2-2000000-2-200000000000000000000
χ4222222222-2-2-2-2-2-22222222222-2-22200000000-2-2-2-20000000000000000-2-200-2-2220000002200000000000000000000
χ4322222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000002-22-20000-22-220000000000000000
χ4422222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000-22-2200002-22-20000000000000000
χ45222-22-2-2-2222-22-22-22-2000000-2-2002-22-22-22-2000022−2−222−2−222−2−222−2−2000000000000000000002−22−22−22−200000000
χ46222-22-2-2-2222-22-22-22-2000000-2-2002-22-22-22-20000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ47222-22-2-2-2222-22-22-22-2000000-2-200-22-22-22-22000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ48222-22-2-2-2222-22-22-22-2000000-2-200-22-22-22-220000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
χ49222-22-2-2-222-22-22-22-22000000-2-2002-22-2-22-22000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ50222-22-2-2-222-22-22-22-22000000-2-2002-22-2-22-220000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ51222-22-2-2-222-22-22-22-22000000-2-200-22-222-22-2000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ52222-22-2-2-222-22-22-22-22000000-2-200-22-222-22-20000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ5322-22-2-2-222-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-222-2-2222-2-22i2i−2i−2i−2i2i-22000000000000000000−2i2i00000000-220000000000000000000000
χ5422-22-2-2-222-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-222-2-22-2-222−2i−2i2i2i−2i2i-220000000000000000002i−2i000000002-20000000000000000000000
χ5522-22-2-2-222-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-222-2-2222-2-2−2i−2i2i2i2i−2i-220000000000000000002i−2i00000000-220000000000000000000000
χ5622-22-2-2-222-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-222-2-22-2-2222i2i−2i−2i2i−2i-22000000000000000000−2i2i000000002-20000000000000000000000
χ5722-22-2-2-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-22-22-2200000000−2i2i2-20000000000000000000000002i−2i−2i2i00002-2-220000000000000000
χ5822-22-2-2-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-22-22-2200000000−2i2i2-2000000000000000000000000−2i2i2i−2i0000-222-20000000000000000
χ5922-22-2-2-22-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-222-2000000002i−2i-2200000000000000002-200−2i2i2i−2i000000-2200000000000000000000
χ6022-22-2-2-22-222i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-222-2000000002i−2i-220000000000000000-22002i−2i−2i2i0000002-200000000000000000000
χ6122-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-2-222-200000000−2i2i-2200000000000000002-2002i−2i−2i2i000000-2200000000000000000000
χ6222-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-2-222-200000000−2i2i-220000000000000000-2200−2i2i2i−2i0000002-200000000000000000000
χ6322-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-22-22-22000000002i−2i2-20000000000000000000000002i−2i−2i2i0000-222-20000000000000000
χ6422-22-2-2-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-22-22-22000000002i−2i2-2000000000000000000000000−2i2i2i−2i00002-2-220000000000000000
χ6522-2-2-222-22-22i−2i−2i2i2i−2i−2i2i000000-22002-2-222i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000i2−i2−i2i22−2−2200000000
χ6622-2-2-222-22-22i−2i−2i2i2i−2i−2i2i000000-22002-2-222i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000−i2i2i2−i2−222−200000000
χ6722-2-2-222-22-22i−2i−2i2i2i−2i−2i2i000000-2200-222-2−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000−i2i2i2−i2−222−200000000
χ6822-2-2-222-22-22i−2i−2i2i2i−2i−2i2i000000-2200-222-2−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000i2−i2−i2i22−2−2200000000
χ6922-2-2-222-22-2−2i2i2i−2i−2i2i2i−2i000000-22002-2-22−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000i2−i2−i2i2−222−200000000
χ7022-2-2-222-22-2−2i2i2i−2i−2i2i2i−2i000000-22002-2-22−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000−i2i2i2−i22−2−2200000000
χ7122-2-2-222-22-2−2i2i2i−2i−2i2i2i−2i000000-2200-222-22i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000−i2i2i2−i22−2−2200000000
χ7222-2-2-222-22-2−2i2i2i−2i−2i2i2i−2i000000-2200-222-22i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000i2−i2−i2i2−222−200000000
χ73444-44-4-4-4-4-44-44-4-44-4400000044000000000000000000000000000000000000000000000000000000000000000000
χ74444-44-4-4-4-4-4-44-444-44-400000044000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-4-444i−4i−4i4i−4i4i4i−4i0000004-4000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4-44−4i4i4i−4i4i−4i−4i4i0000004-4000000000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-400000000004-44-40000000000000000002-22-22-22-22-22-22-22-2000000000000000000000000000000000000
χ784-444-44-4-400000000004-44-4000000000000000000-22-22-22-22-22-22-22-22000000000000000000000000000000000000
χ794-444-44-4-40000000000-44-440000000000000000002-22-22-22-2-22-22-22-22000000000000000000000000000000000000
χ804-444-44-4-40000000000-44-44000000000000000000-22-22-22-222-22-22-22-2000000000000000000000000000000000000
χ814-44-4-4-444000000000000004-400-4400000000000022−22−222222−22−222200000000000000000000000000000000000000000000
χ824-44-4-4-444000000000000004-400-44000000000000−222222−22−222222−2200000000000000000000000000000000000000000000
χ834-44-4-4-44400000000000000-44004-40000000000000000000022−22−222222−22−2222000000000000000000000000000000000000
χ844-44-4-4-44400000000000000-44004-400000000000000000000−222222−22−222222−22000000000000000000000000000000000000
χ854-4-444-44-400000000004i−4i−4i4i0000000000000000002i−2i2i−2i−2i2i−2i2i2-22-2-22-22000000000000000000000000000000000000
χ864-4-444-44-400000000004i−4i−4i4i000000000000000000−2i2i−2i2i2i−2i2i−2i-22-222-22-2000000000000000000000000000000000000
χ874-4-444-44-40000000000−4i4i4i−4i0000000000000000002i−2i2i−2i−2i2i−2i2i-22-222-22-2000000000000000000000000000000000000
χ884-4-444-44-40000000000−4i4i4i−4i000000000000000000−2i2i−2i2i2i−2i2i−2i2-22-2-22-22000000000000000000000000000000000000
χ894-4-4-444-44000000000000004400-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ904-4-4-444-44000000000000004400-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ914-4-4-444-4400000000000000-4-400440000000000000000000022−22−2222−222222−22000000000000000000000000000000000000
χ924-4-4-444-4400000000000000-4-4004400000000000000000000−222222−2222−22−2222000000000000000000000000000000000000

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