Finite Group Databasebeta

← Group #12159819

Character table — Group #12159819

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107
size11112222222222222244444444444444444444888888888888888888888888888888888888161616161616161616161616161616202020204040404040404040404040404040
order1222224444551010101010102244444410101010202020202020202044441010101020202020202020202020202020202020202020202020202020202020288101010104040404040404040888824444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1111-1-1-1
χ41111111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1111
χ51111111111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-1111111-1-111111-1-11-1-11-1-1-1
χ81111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111-1-111-1-1-1-1-111-111-1111
χ9111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-111111111-1-11-1-1-1-111111-1-1
χ10111111111111111111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111-11111-1-1-1-1-111
χ11111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-111-1-1-1-1-111-1-1-1111-111
χ12111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1-1-111111-1-1111-1-1-11-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-11-1-1111-1-11-111
χ16111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11111-111-1-1-111-11-1-1
χ172222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ182222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-2-2-21−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000
χ192222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ202222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+522-22−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ212222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ222222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5222-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ232222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000000
χ242222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+52-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ252222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ262222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-2-2-21+521+521−521−521+521+521−521−521+521+521−521−52000000000000000000
χ272222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-22-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ282222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−522-22−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ292222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ302222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5222-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ312222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222221+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+522-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000000
χ322222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-2221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ332222-2-22-2-2222222222000022-2-2-2-2-2-22-22-22-22-20000000022220000-2-2-2-20000000000000000000000000000000002200-200002000-200
χ342222-2-22-2-2222222222000022-2-2-2-2-2-22-22-22-22-20000000022220000-2-2-2-2000000000000000000000000000000000-2-20020000-2000200
χ352222-2-22-2-22222222220000-2-222-2-2-2-22-22-22-22-200000000-2-2-2-200002222000000000000000000000000000000000220020000-2000-200
χ362222-2-22-2-22222222220000-2-222-2-2-2-22-22-22-22-200000000-2-2-2-200002222000000000000000000000000000000000-2-200-200002000200
χ372222-2-2-222-22222222222-2-20000-2-2-2-2-22-22-22-22000022220000-2-2-2-20000000000000000000000000000000000022002-200000000-2000
χ382222-2-2-222-22222222222-2-20000-2-2-2-2-22-22-22-22000022220000-2-2-2-200000000000000000000000000000000000-2-200-22000000002000
χ392222-2-2-222-222222222-2-2220000-2-2-2-2-22-22-22-220000-2-2-2-200002222000000000000000000000000000000000002200-2200000000-2000
χ402222-2-2-222-222222222-2-2220000-2-2-2-2-22-22-22-220000-2-2-2-20000222200000000000000000000000000000000000-2-2002-2000000002000
χ4122-2-22-2-2-22222-2-222-2-22-22-22i−2i2i−2i22-2-22-22-2-22-222i−2i002-22-22i−2i2i−2i2-22-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000
χ4222-2-22-2-2-22222-2-222-2-22-22-2−2i2i−2i2i22-2-22-22-2-22-22−2i2i002-22-2−2i2i−2i2i2-22-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000
χ4322-2-22-2-2-22222-2-222-2-2-22-222i−2i2i−2i22-2-22-22-2-22-22−2i2i00-22-222i−2i2i−2i-22-222i−2i2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000
χ4422-2-22-2-2-22222-2-222-2-2-22-22−2i2i−2i2i22-2-22-22-2-22-222i−2i00-22-22−2i2i−2i2i-22-22−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000
χ4522-2-22-2-2-222−1+52−1−521−521+52−1+52−1−521−521+522-22-22i−2i2i−2i−1+52−1−521−521+52−1+521−52−1−521+521−52−1+521+52−1−522i−2i00−1+521−52−1−521+52−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−1+521−52−1−521+52−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000000000000
χ4622-2-22-2-2-222−1+52−1−521−521+52−1+52−1−521−521+522-22-22i−2i2i−2i−1+52−1−521−521+52−1+521−52−1−521+521−52−1+521+52−1−522i−2i00−1+521−52−1−521+52−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−1+521−52−1−521+52−ζ22−ζ38ζ22+ζ38−ζ6−ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ14−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000000000
χ4722-2-22-2-2-222−1+52−1−521−521+52−1+52−1−521−521+522-22-2−2i2i−2i2i−1+52−1−521−521+52−1+521−52−1−521+521−52−1+521+52−1−52−2i2i00−1+521−52−1−521+52ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14−1+521−52−1−521+52ζ22+ζ38−ζ22−ζ38ζ6+ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ14−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000000000000
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χ998-88-8000000−2+25−2−25−2+25−2−252−252+252−252+2500000000000000000000004i−4i000000000000000000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14−2ζ6−2ζ142ζ6+2ζ14000000000000000000000000000000000
χ1008-88-8000000−2+25−2−25−2+25−2−252−252+252−252+250000000000000000000000−4i4i0000000000000000000000002ζ22+2ζ38−2ζ22−2ζ382ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ142ζ6+2ζ14−2ζ6−2ζ14000000000000000000000000000000000
χ1018-88-8000000−2−25−2+25−2−25−2+252+252−252+252−2500000000000000000000004i−4i000000000000000000000000−2ζ6−2ζ142ζ6+2ζ14−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38−2ζ22−2ζ382ζ22+2ζ38000000000000000000000000000000000
χ1028-88-8000000−2−25−2+25−2−25−2+252+252−252+252−250000000000000000000000−4i4i0000000000000000000000002ζ6+2ζ14−2ζ6−2ζ142ζ6+2ζ14−2ζ6−2ζ142ζ22+2ζ38−2ζ22−2ζ382ζ22+2ζ38−2ζ22−2ζ38000000000000000000000000000000000
χ1038-8-8800000088-8-8-8-88800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88000000−2+25−2−252−252+252−252+25−2+25−2−250000000000000000000000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000000
χ1058-8-88000000−2+25−2−252−252+252−252+25−2+25−2−25000000000000000000000000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000000
χ1068-8-88000000−2−25−2+252+252−252+252−25−2−25−2+25000000000000000000000000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ362ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000000
χ1078-8-88000000−2−25−2+252+252−252+252−25−2−25−2+250000000000000000000000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ36−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.