Finite Group Databasebeta

← Group #193221

Character table — Group #193221

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222244444444444444444444444444448888888888888888222244444444444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111111111-1-1-1-1
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-11-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ17111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11ii−i−iii−i−i-1iiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−i11-1-1ii−i−ii−ii−i11-1-111-1-1i−ii−i1-11-1
χ18111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11ii−i−iii−i−i-1iiii−i−i−i−iiiii−i−i−i−i-1-111−iii−i-1-111−i−iiii−i−ii11-1-111-1-1−ii−ii-11-11
χ19111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11ii−i−iii−i−i-1−i−i−i−iiiii−i−i−i−iiiii11-1-1i−ii−i11-1-1ii−i−ii−ii−i-1-111-1-111−ii−ii-11-11
χ20111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11ii−i−iii−i−i-1−i−i−i−iiiii−i−i−i−iiiii-1-111−iii−i-1-111−i−iiii−i−ii-1-111-1-111i−ii−i1-11-1
χ21111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11−i−iii−i−iii-1iiii−i−i−i−iiiii−i−i−i−i11-1-1−ii−ii11-1-1−i−iii−ii−ii-1-111-1-111i−ii−i-11-11
χ22111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11−i−iii−i−iii-1iiii−i−i−i−iiiii−i−i−i−i-1-111i−i−ii-1-111ii−i−i−iii−i-1-111-1-111−ii−ii1-11-1
χ23111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11−i−iii−i−iii-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii11-1-1−i−iii−ii−ii11-1-111-1-1−ii−ii1-11-1
χ24111-11-1-1-111-1-11-1-1-1-111-1-111-1-11111-11−i−iii−i−iii-1−i−i−i−iiiii−i−i−i−iiiii-1-111i−i−ii-1-111ii−i−i−iii−i11-1-111-1-1i−ii−i-11-11
χ25111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111ii−i−i−i−iii-1iiii−i−i−i−i−i−i−i−iiiii11-1-1−ii−ii-1-111ii−i−ii−i−ii11-1-1-1-111i−i−ii1-1-11
χ26111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111ii−i−i−i−iii-1iiii−i−i−i−i−i−i−i−iiiii-1-111i−i−ii11-1-1−i−iiii−ii−i11-1-1-1-111−iii−i-111-1
χ27111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111ii−i−i−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−ii−ii-1-111ii−i−ii−i−ii-1-11111-1-1−iii−i-111-1
χ28111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111ii−i−i−i−iii-1−i−i−i−iiiiiiiii−i−i−i−i-1-111i−i−ii11-1-1−i−iiii−ii−i-1-11111-1-1i−i−ii1-1-11
χ29111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111−i−iiiii−i−i-1iiii−i−i−i−i−i−i−i−iiiii11-1-1i−ii−i-1-111−i−iii−iii−i-1-11111-1-1i−i−ii-111-1
χ30111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111−i−iiiii−i−i-1iiii−i−i−i−i−i−i−i−iiiii-1-111−iii−i11-1-1ii−i−i−ii−ii-1-11111-1-1−iii−i1-1-11
χ31111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111−i−iiiii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1i−ii−i-1-111−i−iii−iii−i11-1-1-1-111−iii−i1-1-11
χ32111-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111-111−i−iiiii−i−i-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−iii−i11-1-1ii−i−i−ii−ii11-1-1-1-111i−i−ii-111-1
χ33222222222222222-2-22222-2-2-2-2-2-22-2-2-200000000-200000000000000000000220000002-22-200-2-20000000000000000
χ34222222222222222-2-22222-2-2-2-2-2-22-2-2-200000000-200000000000000000000-2-2000000-22-2200220000000000000000
χ35222222222222-2-2-222-2-2-2-2-2-2-2-222-222-22222-2-2-2-2-200000000000000000000002200000000-2-2000000000000000000
χ36222222222222-2-2-222-2-2-2-2-2-2-2-222-222-2-2-2-2-22222-20000000000000000000000-2-20000000022000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2200000000200000000000000002-22-200002-22-2000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-220000000020000000000000000-22-220000-22-22000000000000000000000000
χ3922222222-2-2-2-2222-2-2-2-2-2-22222-2-2222-200000000-20000000000000000000022000000-22-2200-2-20000000000000000
χ4022222222-2-2-2-2222-2-2-2-2-2-22222-2-2222-200000000-200000000000000000000-2-20000002-22-200220000000000000000
χ4122222222-2-2-2-2-2-2-2222222222222-2-2-2-222222222-20000000000000000000000-2-200000000-2-2000000000000000000
χ4222222222-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000220000000022000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-222200000000200000000000000002-22-20000-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22220000000020000000000000000-22-2200002-22-2000000000000000000000000
χ45222-22-2-2-222-2-22-2-22222-2-2-2-222-2-22-22-2000000002000000000000000000002i−2i0000002i−2i−2i2i00−2i2i0000000000000000
χ46222-22-2-2-222-2-22-2-22222-2-2-2-222-2-22-22-200000000200000000000000000000−2i2i000000−2i2i2i−2i002i−2i0000000000000000
χ47222-22-2-2-222-2-2-22222-2-22222-2-2-2-2-2-22200000000-200000000000000002-2-2200002-2-22000000000000000000000000
χ48222-22-2-2-222-2-2-22222-2-22222-2-2-2-2-2-22200000000-20000000000000000-222-20000-222-2000000000000000000000000
χ49222-22-2-2-222-2-2-222-2-2-2-222-2-22222-22-2-22i2i−2i−2i−2i−2i2i2i200000000000000000000002i−2i00000000−2i2i000000000000000000
χ50222-22-2-2-222-2-2-222-2-2-2-222-2-22222-22-2-2−2i−2i2i2i2i2i−2i−2i20000000000000000000000−2i2i000000002i−2i000000000000000000
χ51222-22-2-2-2-2-2222-2-222-2-22222-2-2-2-222-2-2000000002000000000000000000002i−2i000000−2i2i2i−2i00−2i2i0000000000000000
χ52222-22-2-2-2-2-2222-2-222-2-22222-2-2-2-222-2-200000000200000000000000000000−2i2i0000002i−2i−2i2i002i−2i0000000000000000
χ53222-22-2-2-2-2-222-2222222-2-2-2-222-2-2-22-2200000000-200000000000000002-2-220000-222-2000000000000000000000000
χ54222-22-2-2-2-2-222-2222222-2-2-2-222-2-2-22-2200000000-20000000000000000-222-200002-2-22000000000000000000000000
χ55222-22-2-2-2-2-222-222-2-222-2-222-2-222-2-22-22i2i−2i−2i2i2i−2i−2i20000000000000000000000−2i2i00000000−2i2i000000000000000000
χ56222-22-2-2-2-2-222-222-2-222-2-222-2-222-2-22-2−2i−2i2i2i−2i−2i2i2i200000000000000000000002i−2i000000002i−2i000000000000000000
χ5722-22-2-2-2200000002-22i−2i2i−2i2i−2i2i−2i2-200002i−2i2i−2i2-22-20i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000002−22−2i2−i2i2−i200000000
χ5822-22-2-2-2200000002-22i−2i2i−2i2i−2i2i−2i2-200002i−2i2i−2i2-22-20−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000000000000000−22−22−i2i2−i2i200000000
χ5922-22-2-2-2200000002-22i−2i2i−2i2i−2i2i−2i2-20000−2i2i−2i2i-22-220i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000−22−22−i2i2−i2i200000000
χ6022-22-2-2-2200000002-22i−2i2i−2i2i−2i2i−2i2-20000−2i2i−2i2i-22-220−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000002−22−2i2−i2i2−i200000000
χ6122-22-2-2-2200000002-2−2i2i−2i2i−2i2i−2i2i2-200002i−2i2i−2i-22-220i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000002−22−2−i2i2−i2i200000000
χ6222-22-2-2-2200000002-2−2i2i−2i2i−2i2i−2i2i2-200002i−2i2i−2i-22-220−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000000000000000−22−22i2−i2i2−i200000000
χ6322-22-2-2-2200000002-2−2i2i−2i2i−2i2i−2i2i2-20000−2i2i−2i2i2-22-20i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000000000000000−22−22i2−i2i2−i200000000
χ6422-22-2-2-2200000002-2−2i2i−2i2i−2i2i−2i2i2-20000−2i2i−2i2i2-22-20−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000002−22−2−i2i2−i2i200000000
χ6522-2-2-222-20000000-222i−2i−2i2i2i−2i−2i2i2-200002-2-22−2i2i2i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22i2−i2−i2i200000000
χ6622-2-2-222-20000000-222i−2i−2i2i2i−2i−2i2i2-200002-2-22−2i2i2i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2−i2i2i2−i200000000
χ6722-2-2-222-20000000-222i−2i−2i2i2i−2i−2i2i2-20000-222-22i−2i−2i2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2−i2i2i2−i200000000
χ6822-2-2-222-20000000-222i−2i−2i2i2i−2i−2i2i2-20000-222-22i−2i−2i2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22i2−i2−i2i200000000
χ6922-2-2-222-20000000-22−2i2i2i−2i−2i2i2i−2i2-200002-2-222i−2i−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000000000002−2−22−i2i2i2−i200000000
χ7022-2-2-222-20000000-22−2i2i2i−2i−2i2i2i−2i2-200002-2-222i−2i−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000000−222−2i2−i2−i2i200000000
χ7122-2-2-222-20000000-22−2i2i2i−2i−2i2i2i−2i2-20000-222-2−2i2i2i−2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000000−222−2i2−i2−i2i200000000
χ7222-2-2-222-20000000-22−2i2i2i−2i−2i2i2i−2i2-20000-222-2−2i2i2i−2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000000000002−2−22−i2i2i2−i200000000
χ7344-44-4-4-440000000-444i−4i4i−4i−4i4i−4i4i-4400000000000000000000000000000000000000000000000000000000000000000
χ7444-44-4-4-440000000-44−4i4i−4i4i4i−4i4i−4i-4400000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-400000004-44i−4i−4i4i−4i4i4i−4i-4400000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-400000004-4−4i4i4i−4i4i−4i−4i4i-4400000000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-4000044-4000000000000-400000000000022−2222−2222−2222−2200000000000000000000000000000000000000000000
χ784-444-44-4-4000044-4000000000000-4000000000000−2222−2222−2222−222200000000000000000000000000000000000000000000
χ794-444-44-4-40000-4-440000000000004000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ804-444-44-4-40000-4-44000000000000400000000000000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ814-44-4-4-44400004-44000000000000-40000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ824-44-4-4-44400004-44000000000000-4000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ834-44-4-4-4440000-44-400000000000040000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000
χ844-44-4-4-4440000-44-4000000000000400000000000000000000−2222−222222−2222−22000000000000000000000000000000000000
χ854-4-444-44-44-44-400000000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ864-4-444-44-44-44-40000000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ874-4-444-44-4-44-4400000000000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ884-4-444-44-4-44-440000000000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ894-4-4-444-444-4-4400000000000000000000000000002-2-22-222-22-2-22-222-2000000000000000000000000000000000000
χ904-4-4-444-444-4-440000000000000000000000000000-222-22-2-22-222-22-2-22000000000000000000000000000000000000
χ914-4-4-444-44-444-400000000000000000000000000002-2-22-222-2-222-22-2-22000000000000000000000000000000000000
χ924-4-4-444-44-444-40000000000000000000000000000-222-22-2-222-2-22-222-2000000000000000000000000000000000000

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