Finite Group Databasebeta

← Group #209751

Character table — Group #209751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222444444444444444444442222444444448888888888888888444444444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1111111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-111
χ1711-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-111-1-1ii−i−ii−i1-1iiii−i−i−i−i1111-1-1-1-111-1-11-1i−i1-1i−iii−i−i1-1i−iii−i−i11-1-1i−i1-1i−i1-1
χ1811-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-111-1-1ii−i−ii−i1-1iiii−i−i−i−i1111-1-1-1-1-1-111-11−ii1-1i−i−i−iii-11−iiii−i−i11-1-1−ii-11−ii-11
χ1911-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-111-1-1ii−i−ii−i1-1−i−i−i−iiiii-1-1-1-1111111-1-11-1i−i1-1i−iii−i−i1-1i−i−i−iii-1-111−ii-11−ii-11
χ2011-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-111-1-1ii−i−ii−i1-1−i−i−i−iiiii-1-1-1-11111-1-111-11−ii1-1i−i−i−iii-11−ii−i−iii-1-111i−i1-1i−i1-1
χ2111-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1-1-111−i−iiii−i1-1iiii−i−i−i−i1111-1-1-1-111-1-1-11−ii-11−iiii−i−i-11−ii−i−iii-1-111i−i1-1−ii-11
χ2211-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1-1-111−i−iiii−i1-1iiii−i−i−i−i1111-1-1-1-1-1-1111-1i−i-11−ii−i−iii1-1i−i−i−iii-1-111−ii-11i−i1-1
χ2311-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1-1-111−i−iiii−i1-1−i−i−i−iiiii-1-1-1-1111111-1-1-11−ii-11−iiii−i−i-11−iiii−i−i11-1-1−ii-11i−i1-1
χ2411-1-11-11-11-1ii−i−iii−i−i1-1ii−i−i1-11-1-1-111−i−iiii−i1-1−i−i−i−iiiii-1-1-1-11111-1-1111-1i−i-11−ii−i−iii1-1i−iii−i−i11-1-1i−i1-1−ii-11
χ2511-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-111-1-1−i−iii−ii1-1iiii−i−i−i−i-1-1-1-1111111-1-11-1−ii1-1−ii−i−iii1-1−iiii−i−i-1-111i−i-11i−i-11
χ2611-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-111-1-1−i−iii−ii1-1iiii−i−i−i−i-1-1-1-11111-1-111-11i−i1-1−iiii−i−i-11i−iii−i−i-1-111−ii1-1−ii1-1
χ2711-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-111-1-1−i−iii−ii1-1−i−i−i−iiiii1111-1-1-1-111-1-11-1−ii1-1−ii−i−iii1-1−ii−i−iii11-1-1−ii1-1−ii1-1
χ2811-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-111-1-1−i−iii−ii1-1−i−i−i−iiiii1111-1-1-1-1-1-111-11i−i1-1−iiii−i−i-11i−i−i−iii11-1-1i−i-11i−i-11
χ2911-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-1-1-111ii−i−i−ii1-1iiii−i−i−i−i-1-1-1-1111111-1-1-11i−i-11i−i−i−iii-11i−i−i−iii11-1-1i−i-11−ii1-1
χ3011-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-1-1-111ii−i−i−ii1-1iiii−i−i−i−i-1-1-1-11111-1-1111-1−ii-11i−iii−i−i1-1−ii−i−iii11-1-1−ii1-1i−i-11
χ3111-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-1-1-111ii−i−i−ii1-1−i−i−i−iiiii1111-1-1-1-111-1-1-11i−i-11i−i−i−iii-11i−iii−i−i-1-111−ii1-1i−i-11
χ3211-1-11-11-11-1−i−iii−i−iii1-1−i−iii1-11-1-1-111ii−i−i−ii1-1−i−i−i−iiiii1111-1-1-1-1-1-1111-1−ii-11i−iii−i−i1-1−iiii−i−i-1-111i−i-11−ii1-1
χ33222222222222222222-2-2-2-2-2-222-2-222222222-2-2-2-2000000000000000000000000-2-2-2-2000000000000000000000000
χ34222222222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-222-2-2000000000000000000000000-2-222000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2222222-2-200000000000000000000000022-2-2000000000000000000000000
χ3722222222-2-22222-2-2-2-222-2-2-2-2-2-2220000000022-2-200000000000000000000222200000000-2-2-2-20000000000000000
χ3822222222-2-22222-2-2-2-222-2-2-2-2-2-2220000000022-2-200000000000000000000-2-2-2-20000000022220000000000000000
χ3922222222-2-22222-2-2-2-2-2-22222-2-2-2-200000000-2-22200000000000000002-22-2000000002-22-200000000000000000000
χ4022222222-2-22222-2-2-2-2-2-22222-2-2-2-200000000-2-2220000000000000000-22-2200000000-22-2200000000000000000000
χ4122222222-2-2-2-2-2-22222222222-2-22200000000-2-2-2-20000000000000000000022-2-200000000-2-2220000000000000000
χ4222222222-2-2-2-2-2-22222222222-2-22200000000-2-2-2-200000000000000000000-2-2220000000022-2-20000000000000000
χ4322222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000222200000000000000002-22-200000000-22-2200000000000000000000
χ4422222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-22-22000000002-22-200000000000000000000
χ452222-2-2-2-2222-22-22-22-2000000-2-2002-22-22-22-2000022−2−222−2−222−2−222−2−2000000000000000000002−22−22−22−200000000
χ462222-2-2-2-2222-22-22-22-2000000-2-2002-22-22-22-20000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ472222-2-2-2-2222-22-22-22-2000000-2-200-22-22-22-22000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ482222-2-2-2-2222-22-22-22-2000000-2-200-22-22-22-220000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
χ492222-2-2-2-222-22-22-22-22000000-2-2002-22-2-22-22000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ502222-2-2-2-222-22-22-22-22000000-2-2002-22-2-22-220000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ512222-2-2-2-222-22-22-22-22000000-2-200-22-222-22-2000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ522222-2-2-2-222-22-22-22-22000000-2-200-22-222-22-20000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ5322-2-22-22-22-22i2i−2i−2i2i2i−2i−2i-22−2i−2i2i2i2-2-2222-2-22i2i−2i−2i−2i2i-22000000000000000000000000-22−2i2i000000000000000000000000
χ5422-2-22-22-22-22i2i−2i−2i2i2i−2i−2i-22−2i−2i2i2i2-2-22-2-222−2i−2i2i2i−2i2i-220000000000000000000000002-22i−2i000000000000000000000000
χ5522-2-22-22-22-2−2i−2i2i2i−2i−2i2i2i-222i2i−2i−2i2-2-2222-2-2−2i−2i2i2i2i−2i-22000000000000000000000000-222i−2i000000000000000000000000
χ5622-2-22-22-22-2−2i−2i2i2i−2i−2i2i2i-222i2i−2i−2i2-2-22-2-2222i2i−2i−2i2i−2i-220000000000000000000000002-2−2i2i000000000000000000000000
χ5722-2-22-22-2-222i2i−2i−2i−2i−2i2i2i2-2−2i−2i2i2i-222-2000000002i−2i-22000000000000000000002-22i−2i00000000-22−2i2i0000000000000000
χ5822-2-22-22-2-222i2i−2i−2i−2i−2i2i2i2-2−2i−2i2i2i-222-2000000002i−2i-2200000000000000000000-22−2i2i000000002-22i−2i0000000000000000
χ5922-2-22-22-2-222i2i−2i−2i−2i−2i2i2i-222i2i−2i−2i-22-2200000000−2i2i2-200000000000000002-2-22000000002i−2i−2i2i00000000000000000000
χ6022-2-22-22-2-222i2i−2i−2i−2i−2i2i2i-222i2i−2i−2i-22-2200000000−2i2i2-20000000000000000-222-200000000−2i2i2i−2i00000000000000000000
χ6122-2-22-22-2-22−2i−2i2i2i2i2i−2i−2i2-22i2i−2i−2i-222-200000000−2i2i-22000000000000000000002-2−2i2i00000000-222i−2i0000000000000000
χ6222-2-22-22-2-22−2i−2i2i2i2i2i−2i−2i2-22i2i−2i−2i-222-200000000−2i2i-2200000000000000000000-222i−2i000000002-2−2i2i0000000000000000
χ6322-2-22-22-2-22−2i−2i2i2i2i2i−2i−2i-22−2i−2i2i2i-22-22000000002i−2i2-200000000000000002-2-2200000000−2i2i2i−2i00000000000000000000
χ6422-2-22-22-2-22−2i−2i2i2i2i2i−2i−2i-22−2i−2i2i2i-22-22000000002i−2i2-20000000000000000-222-2000000002i−2i−2i2i00000000000000000000
χ6522-2-2-22-222-22i−2i−2i2i2i−2i−2i2i000000-22002-2-222i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000i2−i2−i2i22−2−2200000000
χ6622-2-2-22-222-22i−2i−2i2i2i−2i−2i2i000000-22002-2-222i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000−i2i2i2−i2−222−200000000
χ6722-2-2-22-222-22i−2i−2i2i2i−2i−2i2i000000-2200-222-2−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000000000000000−i2i2i2−i2−222−200000000
χ6822-2-2-22-222-22i−2i−2i2i2i−2i−2i2i000000-2200-222-2−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000000000000000i2−i2−i2i22−2−2200000000
χ6922-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000-22002-2-22−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000i2−i2−i2i2−222−200000000
χ7022-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000-22002-2-22−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000−i2i2i2−i22−2−2200000000
χ7122-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000-2200-222-22i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000000000000000−i2i2i2−i22−2−2200000000
χ7222-2-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000-2200-222-22i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000000000000000i2−i2−i2i2−222−200000000
χ734444-4-4-4-4-4-44-44-4-44-4400000044000000000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-4-4-44-444-44-400000044000000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-44-444i−4i−4i4i−4i4i4i−4i0000004-4000000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-44-44-44−4i4i4i−4i4i−4i−4i4i0000004-4000000000000000000000000000000000000000000000000000000000000000000
χ774-44-44-4-440000000000004-44-400000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ784-44-44-4-440000000000004-44-40000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ794-44-44-4-44000000000000-44-4400000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ804-44-44-4-44000000000000-44-440000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ814-44-4-444-400000000004-4000000-44000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ824-44-4-444-400000000004-4000000-4400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ834-44-4-444-40000000000-440000004-40000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ844-44-4-444-40000000000-440000004-4000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ854-4-4444-4-40000000000004i−4i−4i4i00000000000000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ864-4-4444-4-40000000000004i−4i−4i4i0000000000000000-22-222-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ874-4-4444-4-4000000000000−4i4i4i−4i00000000000000002-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ884-4-4444-4-4000000000000−4i4i4i−4i0000000000000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ894-4-44-4-444000000000044000000-4-4000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ904-4-44-4-444000000000044000000-4-400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ914-4-44-4-4440000000000-4-40000004400000000000022−22−2222−222222−2200000000000000000000000000000000000000000000
χ924-4-44-4-4440000000000-4-400000044000000000000−222222−2222−22−222200000000000000000000000000000000000000000000

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