Finite Group Databasebeta

← Group #375650

Character table — Group #375650

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order12222222222244444444444444444444444444444444444444448888888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
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
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-1111-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-1-1-1111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-1-1-1111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-1111-1-1-1
χ91111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-11-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111-111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-111
χ121111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-11-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111
χ17111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-11-1-11-1
χ18111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-11-111-11
χ19111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-111-1-111-1-111-1-1-1-11-111-11
χ20111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-11111-11-1-11-1
χ21111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-1-11-11-11
χ22111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-111-11-11-1
χ23111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-111-11-11-1
χ24111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-1-11-11-11
χ25111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-11
χ26111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-111-1
χ27111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111-111-1
χ28111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-11-1-11
χ29111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-1-1111-1
χ30111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-1111-1-1-11
χ31111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-1111-1-1-11
χ32111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-1-1111-1
χ3322222222-2-2-2-222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ3422222222-2-2-2-222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-222-2-20000000000000000000000000000000000000000
χ3522222222-2-2-2-22222-2-2-2-22222222222-2-2-2-222-2-222-2-222-2-222-2-2-2-20000000000000000000000000000000000000000
χ3622222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222220000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-22222220000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2222222222222-2-222-2-222-2-2-2-222-2-2-2-20000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-222222222-2-222-2-222-2-20000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ41222-2-22-2-222-2-200002i2i−2i−2i2-200002i2i−2i−2i22-2-22-2002i−2i00000000002i−2i0000000000000000002-2002i−2i002-2002i−2i00000000
χ42222-2-22-2-222-2-200002i2i−2i−2i2-200002i2i−2i−2i22-2-22-2002i−2i00000000002i−2i000000000000000000-2200−2i2i00-2200−2i2i00000000
χ43222-2-22-2-222-2-200002i2i−2i−2i-220000−2i−2i2i2i-2-222-22002i−2i0000000000−2i2i0000000000000000002i−2i00-2200−2i2i002-200000000
χ44222-2-22-2-222-2-200002i2i−2i−2i-220000−2i−2i2i2i-2-222-22002i−2i0000000000−2i2i000000000000000000−2i2i002-2002i−2i00-2200000000
χ45222-2-22-2-222-2-20000−2i−2i2i2i2-20000−2i−2i2i2i22-2-22-200−2i2i0000000000−2i2i0000000000000000002-200−2i2i002-200−2i2i00000000
χ46222-2-22-2-222-2-20000−2i−2i2i2i2-20000−2i−2i2i2i22-2-22-200−2i2i0000000000−2i2i000000000000000000-22002i−2i00-22002i−2i00000000
χ47222-2-22-2-222-2-20000−2i−2i2i2i-2200002i2i−2i−2i-2-222-2200−2i2i00000000002i−2i0000000000000000002i−2i002-200−2i2i00-2200000000
χ48222-2-22-2-222-2-20000−2i−2i2i2i-2200002i2i−2i−2i-2-222-2200−2i2i00000000002i−2i000000000000000000−2i2i00-22002i−2i002-200000000
χ49222-2-22-2-2-2-22200002i2i−2i−2i2-20000−2i−2i2i2i-2-2222-200−2i2i00000000002i−2i00000000000000002i−2i002-2002i−2i002-20000000000
χ50222-2-22-2-2-2-22200002i2i−2i−2i2-20000−2i−2i2i2i-2-2222-200−2i2i00000000002i−2i0000000000000000−2i2i00-2200−2i2i00-220000000000
χ51222-2-22-2-2-2-22200002i2i−2i−2i-2200002i2i−2i−2i22-2-2-2200−2i2i0000000000−2i2i00000000000000002-200−2i2i00-22002i−2i0000000000
χ52222-2-22-2-2-2-22200002i2i−2i−2i-2200002i2i−2i−2i22-2-2-2200−2i2i0000000000−2i2i0000000000000000-22002i−2i002-200−2i2i0000000000
χ53222-2-22-2-2-2-2220000−2i−2i2i2i2-200002i2i−2i−2i-2-2222-2002i−2i0000000000−2i2i00000000000000002i−2i00-22002i−2i00-220000000000
χ54222-2-22-2-2-2-2220000−2i−2i2i2i2-200002i2i−2i−2i-2-2222-2002i−2i0000000000−2i2i0000000000000000−2i2i002-200−2i2i002-20000000000
χ55222-2-22-2-2-2-2220000−2i−2i2i2i-220000−2i−2i2i2i22-2-2-22002i−2i00000000002i−2i00000000000000002-2002i−2i00-2200−2i2i0000000000
χ56222-2-22-2-2-2-2220000−2i−2i2i2i-220000−2i−2i2i2i22-2-2-22002i−2i00000000002i−2i0000000000000000-2200−2i2i002-2002i−2i0000000000
χ5722-22-2-22-22-22-22i2i−2i−2i00002-22i2i−2i−2i00002-22-2-222i−2i00000000002i−2i0000002i−2i2-200002i−2i2-2000000000000000000000000
χ5822-22-2-22-22-22-22i2i−2i−2i00002-22i2i−2i−2i00002-22-2-222i−2i00000000002i−2i000000−2i2i-220000−2i2i-22000000000000000000000000
χ5922-22-2-22-22-22-22i2i−2i−2i0000-22−2i−2i2i2i0000-22-222-22i−2i0000000000−2i2i0000002-2−2i2i0000-222i−2i000000000000000000000000
χ6022-22-2-22-22-22-22i2i−2i−2i0000-22−2i−2i2i2i0000-22-222-22i−2i0000000000−2i2i000000-222i−2i00002-2−2i2i000000000000000000000000
χ6122-22-2-22-22-22-2−2i−2i2i2i00002-2−2i−2i2i2i00002-22-2-22−2i2i0000000000−2i2i0000002i−2i-2200002i−2i-22000000000000000000000000
χ6222-22-2-22-22-22-2−2i−2i2i2i00002-2−2i−2i2i2i00002-22-2-22−2i2i0000000000−2i2i000000−2i2i2-20000−2i2i2-2000000000000000000000000
χ6322-22-2-22-22-22-2−2i−2i2i2i0000-222i2i−2i−2i0000-22-222-2−2i2i00000000002i−2i0000002-22i−2i0000-22−2i2i000000000000000000000000
χ6422-22-2-22-22-22-2−2i−2i2i2i0000-222i2i−2i−2i0000-22-222-2−2i2i00000000002i−2i000000-22−2i2i00002-22i−2i000000000000000000000000
χ6522-22-2-22-2-22-222i2i−2i−2i00002-22i2i−2i−2i0000-22-22-22−2i2i0000000000−2i2i002-22i−2i00002-22i−2i0000000000000000000000000000
χ6622-22-2-22-2-22-222i2i−2i−2i00002-22i2i−2i−2i0000-22-22-22−2i2i0000000000−2i2i00-22−2i2i0000-22−2i2i0000000000000000000000000000
χ6722-22-2-22-2-22-222i2i−2i−2i0000-22−2i−2i2i2i00002-22-22-2−2i2i00000000002i−2i002i−2i-220000−2i2i2-20000000000000000000000000000
χ6822-22-2-22-2-22-222i2i−2i−2i0000-22−2i−2i2i2i00002-22-22-2−2i2i00000000002i−2i00−2i2i2-200002i−2i-220000000000000000000000000000
χ6922-22-2-22-2-22-22−2i−2i2i2i00002-2−2i−2i2i2i0000-22-22-222i−2i00000000002i−2i002-2−2i2i00002-2−2i2i0000000000000000000000000000
χ7022-22-2-22-2-22-22−2i−2i2i2i00002-2−2i−2i2i2i0000-22-22-222i−2i00000000002i−2i00-222i−2i0000-222i−2i0000000000000000000000000000
χ7122-22-2-22-2-22-22−2i−2i2i2i0000-222i2i−2i−2i00002-22-22-22i−2i0000000000−2i2i002i−2i2-20000−2i2i-220000000000000000000000000000
χ7222-22-2-22-2-22-22−2i−2i2i2i0000-222i2i−2i−2i00002-22-22-22i−2i0000000000−2i2i00−2i2i-2200002i−2i2-20000000000000000000000000000
χ7344-4-44-4-444-4-440000000044000000004-4-44-4-400000000000000000000000000000000000000000000000000000000
χ7444-4-44-4-444-4-4400000000-4-400000000-444-44400000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-44-444-4000000004400000000-444-4-4-400000000000000000000000000000000000000000000000000000000
χ7644-4-44-4-44-444-400000000-4-4000000004-4-444400000000000000000000000000000000000000000000000000000000
χ774-444-4-4-4400004i−4i4i−4i4-44-40000000000000000000000004i−4i0000000000000000000000000000000000000000000000
χ784-444-4-4-4400004i−4i4i−4i-44-44000000000000000000000000−4i4i0000000000000000000000000000000000000000000000
χ794-444-4-4-440000−4i4i−4i4i4-44-4000000000000000000000000−4i4i0000000000000000000000000000000000000000000000
χ804-444-4-4-440000−4i4i−4i4i-44-440000000000000000000000004i−4i0000000000000000000000000000000000000000000000
χ814-44-44-44-4000000004i−4i−4i4i004i−4i4i−4i000000000000004-400000000000000000000000000000000000000000000000000
χ824-44-44-44-4000000004i−4i−4i4i00−4i4i−4i4i00000000000000-4400000000000000000000000000000000000000000000000000
χ834-44-44-44-400000000−4i4i4i−4i004i−4i4i−4i00000000000000-4400000000000000000000000000000000000000000000000000
χ844-44-44-44-400000000−4i4i4i−4i00−4i4i−4i4i000000000000004-400000000000000000000000000000000000000000000000000
χ854-4-4444-4-400004-4-4400000000004i−4i4i−4i0000000000004i−4i000000000000000000000000000000000000000000000000
χ864-4-4444-4-400004-4-440000000000−4i4i−4i4i000000000000−4i4i000000000000000000000000000000000000000000000000
χ874-4-4444-4-40000-444-400000000004i−4i4i−4i000000000000−4i4i000000000000000000000000000000000000000000000000
χ884-4-4444-4-40000-444-40000000000−4i4i−4i4i0000000000004i−4i000000000000000000000000000000000000000000000000
χ894-4-4-4-4444000000000000004-4-444-4-4400000000000000004-400000000000000000000000000000000000000000000
χ904-4-4-4-4444000000000000004-4-44-444-40000000000000000-4400000000000000000000000000000000000000000000
χ914-4-4-4-444400000000000000-444-44-4-440000000000000000-4400000000000000000000000000000000000000000000
χ924-4-4-4-444400000000000000-444-4-444-400000000000000004-400000000000000000000000000000000000000000000

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