Finite Group Databasebeta

← Group #72319539

Character table — Group #72319539

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size112222222444444444488888888888888888888816161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232323232326464646464646464
order12222222244444444442222222222224444444442222444444444444444444444488882444444444444444888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ511111111111111111111111-1-1-1-11111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-11111111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ711111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1
χ811111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-1-1-11111
χ9111111111-1-1-1-111111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-111-1-1
χ10111111111-1-1-1-111111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-111-1-111-1-111
χ11111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ12111111111-1-1-1-111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111
χ13111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-111
χ14111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-11111-1-111-1-1
χ15111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ16111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ17111-11-11-1-1ii−i−i1-1111-111-1-111-1-111-1-11-1iii−i−i−i-11-11-11-111-1-1i−iii−i−ii−iii−i−iii−i−iii−i−i1-1i−i1-1i−i11-1-1ii−i−ii−i1-11-11-1i−i1-1i−i1-1i−i
χ18111-11-11-1-1ii−i−i1-1111-111-1-111-1-111-1-11-1iii−i−i−i-11-11-11-111-1-1i−iii−i−ii−iii−i−iii−i−iii−i−i-11−ii-11−ii11-1-1ii−i−i−ii-111-1-11−ii-11−ii-11−ii
χ19111-11-11-1-1ii−i−i1-1111-111-1-111-1-111-1-11-1iii−i−i−i-11-1-11-1111-1-1i−iii−i−ii−iii−i−i−i−iii−i−iii1-1i−i-11−ii-1-111−i−iiii−i-11-111-1−ii-11−ii1-1i−i
χ20111-11-11-1-1ii−i−i1-1111-111-1-111-1-111-1-11-1iii−i−i−i-11-1-11-1111-1-1i−iii−i−ii−iii−i−i−i−iii−i−iii-11−ii1-1i−i-1-111−i−iii−ii1-1-11-11i−i1-1i−i-11−ii
χ21111-11-11-1-1ii−i−i1-1111-111-1-1-1-11111-1-11-1iii−i−i−i-1-111-11-1-1-111i−i−i−iiii−i−i−iiiii−i−iii−i−i1-1i−i1-1i−i-1-111−i−iiii−i1-11-11-1i−i-11−ii-11−ii
χ22111-11-11-1-1ii−i−i1-1111-111-1-1-1-11111-1-11-1iii−i−i−i-1-111-11-1-1-111i−i−i−iiii−i−i−iiiii−i−iii−i−i-11−ii-11−ii-1-111−i−iii−ii-111-1-11−ii1-1i−i1-1i−i
χ23111-11-11-1-1ii−i−i1-1111-111-1-1-1-11111-1-11-1iii−i−i−i-1-11-11-11-1-111i−i−i−iiii−i−i−iii−i−iii−i−iii1-1i−i-11−ii11-1-1ii−i−ii−i-11-111-1−ii1-1i−i-11−ii
χ24111-11-11-1-1ii−i−i1-1111-111-1-1-1-11111-1-11-1iii−i−i−i-1-11-11-11-1-111i−i−i−iiii−i−i−iii−i−iii−i−iii-11−ii1-1i−i11-1-1ii−i−i−ii1-1-11-11i−i-11−ii1-1i−i
χ25111-11-11-1-1−i−iii1-1111-111-1-111-1-111-1-11-1−i−i−iiii-11-11-11-111-1-1−ii−i−iii−ii−i−iii−i−iii−i−iii1-1−ii1-1−ii11-1-1−i−iii−ii1-11-11-1−ii1-1−ii1-1−ii
χ26111-11-11-1-1−i−iii1-1111-111-1-111-1-111-1-11-1−i−i−iiii-11-11-11-111-1-1−ii−i−iii−ii−i−iii−i−iii−i−iii-11i−i-11i−i11-1-1−i−iiii−i-111-1-11i−i-11i−i-11i−i
χ27111-11-11-1-1−i−iii1-1111-111-1-111-1-111-1-11-1−i−i−iiii-11-1-11-1111-1-1−ii−i−iii−ii−i−iiiii−i−iii−i−i1-1−ii-11i−i-1-111ii−i−i−ii-11-111-1i−i-11i−i1-1−ii
χ28111-11-11-1-1−i−iii1-1111-111-1-111-1-111-1-11-1−i−i−iiii-11-1-11-1111-1-1−ii−i−iii−ii−i−iiiii−i−iii−i−i-11i−i1-1−ii-1-111ii−i−ii−i1-1-11-11−ii1-1−ii-11i−i
χ29111-11-11-1-1−i−iii1-1111-111-1-1-1-11111-1-11-1−i−i−iiii-1-111-11-1-1-111−iiii−i−i−iiii−i−i−i−iii−i−iii1-1−ii1-1−ii-1-111ii−i−i−ii1-11-11-1−ii-11i−i-11i−i
χ30111-11-11-1-1−i−iii1-1111-111-1-1-1-11111-1-11-1−i−i−iiii-1-111-11-1-1-111−iiii−i−i−iiii−i−i−i−iii−i−iii-11i−i-11i−i-1-111ii−i−ii−i-111-1-11i−i1-1−ii1-1−ii
χ31111-11-11-1-1−i−iii1-1111-111-1-1-1-11111-1-11-1−i−i−iiii-1-11-11-11-1-111−iiii−i−i−iiii−i−iii−i−iii−i−i1-1−ii-11i−i11-1-1−i−iii−ii-11-111-1i−i1-1−ii-11i−i
χ32111-11-11-1-1−i−iii1-1111-111-1-1-1-11111-1-11-1−i−i−iiii-1-11-11-11-1-111−iiii−i−i−iiii−i−iii−i−iii−i−i-11i−i1-1−ii11-1-1−i−iiii−i1-1-11-11−ii-11i−i1-1−ii
χ332222222222222222222-2-2-2-20000-2-2-2-2222-2-22-2-220000000000220000-2-20000000000002222000000000000-2-20000-2-20000000000
χ342222222222222222222-2-2-2-20000-2-2-2-2222-2-22-2-220000000000220000-2-2000000000000-2-2-2-2000000000000220000220000000000
χ35222222222222222-2-2222-22-200002-22-2-2-2222222-20022220000-2-20000-2-200002222-2-2-2-200000000000000000000-2-2000000000000
χ36222222222222222-2-2222-22-200002-22-2-2-2222222-200-2-2-2-20000-2-20000-2-20000-2-2-2-222220000000000000000000022000000000000
χ37222222222222222-2-222-22-220000-22-22-2-22-2-22-2-2-20000000000-2-2000022000000000000000022220000000000-2-20000-2-200000000
χ38222222222222222-2-222-22-220000-22-22-2-22-2-22-2-2-20000000000-2-20000220000000000000000-2-2-2-200000000002200002200000000
χ39222222222-2-2-2-2222222-2-2-2-20000-2-2-2-222-222-22220000000000-2-200002200000000000022-2-2000000000000220000-2-20000000000
χ40222222222-2-2-2-2222222-2-2-2-20000-2-2-2-222-222-22220000000000-2-2000022000000000000-2-222000000000000-2-20000220000000000
χ41222222222-2-2-2-222-2-2222-22-200002-22-2-2-2-2-2-2-2-2-2-20022220000220000220000-2-2-2-2222200000000000000000000-2-2000000000000
χ42222222222-2-2-2-222-2-2222-22-200002-22-2-2-2-2-2-2-2-2-2-200-2-2-2-200002200002200002222-2-2-2-20000000000000000000022000000000000
χ43222222222-2-2-2-222-2-222-22-220000-22-22-2-2-222-222-20000000000220000-2-2000000000000000022-2-20000000000-2-200002200000000
χ44222222222-2-2-2-222-2-222-22-220000-22-22-2-2-222-222-20000000000220000-2-20000000000000000-2-2220000000000220000-2-200000000
χ45222-22-22-2-22i2i−2i−2i2-2222-2-2-2220000-2-2222-22i−2i−2i−2i2i2i-200000000002i−2i0000−2i2i0000000000002-22i−2i000000000000−2i2i0000-220000000000
χ46222-22-22-2-22i2i−2i−2i2-2222-2-2-2220000-2-2222-22i−2i−2i−2i2i2i-200000000002i−2i0000−2i2i000000000000-22−2i2i0000000000002i−2i00002-20000000000
χ47222-22-22-2-22i2i−2i−2i2-2-2-22-22-2-2200002-2-22-222i2i2i−2i−2i−2i2002-22-20000−2i2i0000−2i2i00002i2i−2i−2i−2i−2i2i2i00000000000000000000-22000000000000
χ48222-22-22-2-22i2i−2i−2i2-2-2-22-22-2-2200002-2-22-222i2i2i−2i−2i−2i200-22-220000−2i2i0000−2i2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000002-2000000000000
χ49222-22-22-2-22i2i−2i−2i2-2-2-22-2-222-20000-222-2-222i−2i−2i−2i2i2i20000000000−2i2i00002i−2i00000000000000002-22i−2i0000000000-220000−2i2i00000000
χ50222-22-22-2-22i2i−2i−2i2-2-2-22-2-222-20000-222-2-222i−2i−2i−2i2i2i20000000000−2i2i00002i−2i0000000000000000-22−2i2i00000000002-200002i−2i00000000
χ51222-22-22-2-2−2i−2i2i2i2-2222-2-2-2220000-2-2222-2−2i2i2i2i−2i−2i-20000000000−2i2i00002i−2i0000000000002-2−2i2i0000000000002i−2i0000-220000000000
χ52222-22-22-2-2−2i−2i2i2i2-2222-2-2-2220000-2-2222-2−2i2i2i2i−2i−2i-20000000000−2i2i00002i−2i000000000000-222i−2i000000000000−2i2i00002-20000000000
χ53222-22-22-2-2−2i−2i2i2i2-2-2-22-22-2-2200002-2-22-22−2i−2i−2i2i2i2i2002-22-200002i−2i00002i−2i0000−2i−2i2i2i2i2i−2i−2i00000000000000000000-22000000000000
χ54222-22-22-2-2−2i−2i2i2i2-2-2-22-22-2-2200002-2-22-22−2i−2i−2i2i2i2i200-22-2200002i−2i00002i−2i00002i2i−2i−2i−2i−2i2i2i000000000000000000002-2000000000000
χ55222-22-22-2-2−2i−2i2i2i2-2-2-22-2-222-20000-222-2-22−2i2i2i2i−2i−2i200000000002i−2i0000−2i2i00000000000000002-2−2i2i0000000000-2200002i−2i00000000
χ56222-22-22-2-2−2i−2i2i2i2-2-2-22-2-222-20000-222-2-22−2i2i2i2i−2i−2i200000000002i−2i0000−2i2i0000000000000000-222i−2i00000000002-20000−2i2i00000000
χ5722-22-222-2-20000-22222-2-222222-2-22-2-2-2-2-20000002-2200002-22-20000000000002i−2i2i−2i2i−2i2i−2i0000000000002i−2i2i−2i000000000000000000
χ5822-22-222-2-20000-22222-2-222222-2-22-2-2-2-2-20000002-2200002-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000−2i2i−2i2i000000000000000000
χ5922-22-222-2-20000-22222-2-2222-2-2222-2-2-2-2-200000022-20000-22-220000000000002i−2i2i−2i2i−2i2i−2i000000000000−2i2i−2i2i000000000000000000
χ6022-22-222-2-20000-22222-2-2222-2-2222-2-2-2-2-200000022-20000-22-22000000000000−2i2i−2i2i−2i2i−2i2i0000000000002i−2i2i−2i000000000000000000
χ6122-22-222-2-20000-22-2-22-2-2-22-2000022-2222000000-20000000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000002-22-20000000000000000000000
χ6222-22-222-2-20000-22-2-22-2-2-22-2000022-2222000000-20000000000002i−2i2i−2i002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000-22-220000000000000000000000
χ6322-22-222-2-20000-22-2-22-2-2-22-2000022-2222000000-2000000000000−2i2i−2i2i00−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000-22-220000000000000000000000
χ6422-22-222-2-20000-22-2-22-2-2-22-2000022-2222000000-2000000000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000002-22-20000000000000000000000
χ6522-2-2-2-22220000-2-22222-22-2-222222-222-22000000-2-2-200002-2-220000000000002-2-222-2-220000000000002-2-22000000000000000000
χ6622-2-2-2-22220000-2-22222-22-2-222222-222-22000000-2-2-200002-2-22000000000000-222-2-222-2000000000000-222-2000000000000000000
χ6722-2-2-2-22220000-2-22222-22-2-2-2-2-2-22-222-22000000-2220000-222-20000000000002-2-222-2-22000000000000-222-2000000000000000000
χ6822-2-2-2-22220000-2-22222-22-2-2-2-2-2-22-222-22000000-2220000-222-2000000000000-222-2-222-20000000000002-2-22000000000000000000
χ6922-2-2-2-22220000-2-2-2-222-2-2-220000222-22-200000020000000000002-2-22002-2-222-2-22-222-2000000002-2-220000000000000000000000
χ7022-2-2-2-22220000-2-2-2-222-2-2-220000222-22-200000020000000000002-2-22002-2-22-222-22-2-2200000000-222-20000000000000000000000
χ7122-2-2-2-22220000-2-2-2-222-2-2-220000222-22-20000002000000000000-222-200-222-22-2-22-222-200000000-222-20000000000000000000000
χ7222-2-2-2-22220000-2-2-2-222-2-2-220000222-22-20000002000000000000-222-200-222-2-222-22-2-22000000002-2-220000000000000000000000
χ734444444444444-4-400-4-400002222000000-400-4000220000-2-2-2-200-2-2-2-2002222000000000000000000000000000000000000000000
χ744444444444444-4-400-4-40000-2-2-2-2000000-400-4000-2-20000222200222200-2-2-2-2000000000000000000000000000000000000000000
χ75444444444-4-4-4-4-4-400-4-4000022220000004004000220000-2-2-2-200222200-2-2-2-2000000000000000000000000000000000000000000
χ76444444444-4-4-4-4-4-400-4-40000-2-2-2-20000004004000-2-20000222200-2-2-2-2002222000000000000000000000000000000000000000000
χ77444-44-44-4-44i4i−4i−4i-4400-44000022-2-2000000−4i004i0002-20000-2-22200−2i−2i2i2i002i2i−2i−2i000000000000000000000000000000000000000000
χ78444-44-44-4-44i4i−4i−4i-4400-440000-2-222000000−4i004i000-22000022-2-2002i2i−2i−2i00−2i−2i2i2i000000000000000000000000000000000000000000
χ79444-44-44-4-4−4i−4i4i4i-4400-44000022-2-20000004i00−4i0002-20000-2-222002i2i−2i−2i00−2i−2i2i2i000000000000000000000000000000000000000000
χ80444-44-44-4-4−4i−4i4i4i-4400-440000-2-2220000004i00−4i000-22000022-2-200−2i−2i2i2i002i2i−2i−2i000000000000000000000000000000000000000000
χ8144-44-444-4-400004-400-44000022-2-200000004i−4i04i−4i0-220000-22-22002i−2i2i−2i00−2i2i−2i2i000000000000000000000000000000000000000000
χ8244-44-444-4-400004-400-44000022-2-20000000−4i4i0−4i4i0-220000-22-2200−2i2i−2i2i002i−2i2i−2i000000000000000000000000000000000000000000
χ8344-44-444-4-400004-400-440000-2-22200000004i−4i04i−4i02-200002-22-200−2i2i−2i2i002i−2i2i−2i000000000000000000000000000000000000000000
χ8444-44-444-4-400004-400-440000-2-2220000000−4i4i0−4i4i02-200002-22-2002i−2i2i−2i00−2i2i−2i2i000000000000000000000000000000000000000000
χ8544-44-444-4-40000-44444-44-4-4-40000-4444-4-400000040000000000000000000000000000000000000000000000000000000000000000
χ8644-44-444-4-40000-44-4-44-444-440000-4-44-444000000-40000000000000000000000000000000000000000000000000000000000000000
χ8744-4-4-4-444400004400-4-40000222200000004-40-440-2-20000-222-2002-2-2200-222-2000000000000000000000000000000000000000000
χ8844-4-4-4-444400004400-4-4000022220000000-4404-40-2-20000-222-200-222-2002-2-22000000000000000000000000000000000000000000
χ8944-4-4-4-444400004400-4-40000-2-2-2-200000004-40-4402200002-2-2200-222-2002-2-22000000000000000000000000000000000000000000
χ9044-4-4-4-444400004400-4-40000-2-2-2-20000000-4404-402200002-2-22002-2-2200-222-2000000000000000000000000000000000000000000
χ9144-4-4-4-44440000-4-444444-4440000-44-4-4-44000000-40000000000000000000000000000000000000000000000000000000000000000
χ9244-4-4-4-44440000-4-4-4-444444-40000-4-4-444-400000040000000000000000000000000000000000000000000000000000000000000000
χ938888-8-8-88-88i−8i8i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ948888-8-8-88-8−8i8i−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ95888-8-88-8-888-8-880000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ96888-8-88-8-88-888-80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9788-888-8-8-8800000000000000000000000000000000044-4-40000000000000000000000000000000000000000000000000000000000
χ9888-888-8-8-88000000000000000000000000000000000-4-4440000000000000000000000000000000000000000000000000000000000
χ9988-8-888-88-80000000000000000000000000000000004-4-440000000000000000000000000000000000000000000000000000000000
χ10088-8-888-88-8000000000000000000000000000000000-444-40000000000000000000000000000000000000000000000000000000000
χ10116-1600000000000008-8000000008-800000000000000000000000000000000000000000000000000000000000000000000000000000
χ10216-1600000000000008-800000000-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ10316-160000000000000-880000008-80000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10416-160000000000000-88000000-880000000000000000000000000000000000000000000000000000000000000000000000000000000

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