Finite Group Databasebeta

← Group #12016458

Character table — Group #12016458

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222444444444444444488888888888888888888888888161616161616161616161616161616161616161640404040404040404040404040404040
order122222444455101010101010101010101010101044448888202020202020202088202020202020202040404040404040404040404040404040444420202020202020202020202020202020224444441616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ711111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ91-1-111-11-11-1111111-1-1-1-1-1-1-1-111ii−i−i1-11-111-1-111-1-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−iiiii−i−i−i−i1111-1-1-1-11-1ii−i−i1-111-1-1ii−i−i
χ101-1-111-11-11-1111111-1-1-1-1-1-1-1-111ii−i−i1-11-111-1-111-1-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−iiiii−i−i−i−i1111-1-1-1-1-11−i−iii-11-1-111−i−iii
χ111-1-111-11-11-1111111-1-1-1-1-1-1-1-111ii−i−i1-11-111-1-111-1-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii−i−i−i−iiiii-1-1-1-111111-1ii−i−i1-1-1-111−i−iii
χ121-1-111-11-11-1111111-1-1-1-1-1-1-1-111ii−i−i1-11-111-1-111-1-1i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii−i−i−i−iiiii-1-1-1-11111-11−i−iii-1111-1-1ii−i−i
χ131-1-111-11-11-1111111-1-1-1-1-1-1-1-111−i−iii1-11-111-1-111-1-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii−i−i−i−iiiii1111-1-1-1-11-1−i−iii1-111-1-1−i−iii
χ141-1-111-11-11-1111111-1-1-1-1-1-1-1-111−i−iii1-11-111-1-111-1-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii−i−i−i−iiiii1111-1-1-1-1-11ii−i−i-11-1-111ii−i−i
χ151-1-111-11-11-1111111-1-1-1-1-1-1-1-111−i−iii1-11-111-1-111-1-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11i−iiiii−i−i−i−i-1-1-1-111111-1−i−iii1-1-1-111ii−i−i
χ161-1-111-11-11-1111111-1-1-1-1-1-1-1-111−i−iii1-11-111-1-111-1-1−ii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-11i−iiiii−i−i−i−i-1-1-1-11111-11ii−i−i-1111-1-1−i−iii
χ17222222222222222222222222222222-2-2-2-222222222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222−1+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+52−1−5222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−522222−1+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+52−1−52−1−520000000000000000
χ202222222222−1+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+52−1−5222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ212222222222−1+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+52−1−522222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ222222222222−1+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+52−1−522222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ232222222222−1+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+52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-21−521−521+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+5222-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ242222222222−1+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+52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-21−521−521+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+52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ252222222222−1+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+52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52221−521−521+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+52−1−52−1−520000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ262222222222−1+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+52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52221−521−521+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+52−1−52−1−520000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ272222222222−1−52−1+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+5222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+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+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+520000000000000000
χ282222222222−1−52−1+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+5222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1−52−1+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+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ292222222222−1−52−1+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+522222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000000000000
χ302222222222−1−52−1+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+522222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
χ312222222222−1−52−1+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+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-21+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+521−521−5222-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ322222222222−1−52−1+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+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-21+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+521−521−52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000
χ332222222222−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52221+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+520000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
χ342222222222−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52221+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+520000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000000000000
χ35222222-2-2-2-222222222222222222-22-20000-2-2-2-2-2-2-2-2002-22-22-22-2000000000000000000000000000000000000000000002−22−22−22−2
χ36222222-2-2-2-222222222222222222-22-20000-2-2-2-2-2-2-2-2002-22-22-22-200000000000000000000000000000000000000000000−22−22−22−22
χ37222222-2-2-2-22222222222222222-22-220000-2-2-2-2-2-2-2-200-22-22-22-22000000000000000000000000000000000000000000002−22−2−22−22
χ38222222-2-2-2-22222222222222222-22-220000-2-2-2-2-2-2-2-200-22-22-22-2200000000000000000000000000000000000000000000−22−222−22−2
χ392222-2-2-2-22222-2-2-2-22222-2-2-2-22200002-2-22-2-2-2-2222200000000002-22-22-22-20000000000000000000000000000002-22-20000000000
χ402222-2-2-2-22222-2-2-2-22222-2-2-2-22200002-2-22-2-2-2-2222200000000002-22-22-22-2000000000000000000000000000000-22-220000000000
χ412222-2-2-2-22222-2-2-2-22222-2-2-2-2220000-222-2-2-2-2-222220000000000-22-22-22-220000000000000000000000000000220000-2-200000000
χ422222-2-2-2-22222-2-2-2-22222-2-2-2-2220000-222-2-2-2-2-222220000000000-22-22-22-220000000000000000000000000000-2-200002200000000
χ432-2-222-22-22-2222222-2-2-2-2-2-2-2-2222i2i−2i−2i-22-2222-2-222-2-2−2i2i2i2i2i2i−2i−2i−2i−2i-2-2-2-22222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ442-2-222-22-22-2222222-2-2-2-2-2-2-2-222−2i−2i2i2i-22-2222-2-222-2-22i−2i−2i−2i−2i−2i2i2i2i2i-2-2-2-222222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ452-2-222-22-22-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−522i2i−2i−2i2-22-2−1+52−1−521−521+52−1+52−1−521−521+522i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1+52−1−52−1−521−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ142-22i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1+52−1−52−1−521−521−521+521+520000000000000000
χ462-2-222-22-22-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−522i2i−2i−2i2-22-2−1+52−1−521−521+52−1+52−1−521−521+522i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−1+52−1+52−1−52−1−521−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14-22−2i2iζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ141−521−521+521+52−1+52−1+52−1−52−1−520000000000000000
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χ934-4-44-44-444-4−1−5−1+51+51+51−51−51+51+51−51−5−1−5−1−5−1+5−1+5−1−5−1+5000044-4-41+51−5−1−5−1+5−1−5−1+51+51−50000000000−1−51+5−1+51−51+5−1−51−5−1+500000000000000000000000000000000000000000000
χ944-4-44-44-444-4−1−5−1+51+51+51−51−51+51+51−51−5−1−5−1−5−1+5−1+5−1−5−1+50000-4-4441+51−5−1−5−1+5−1−5−1+51+51−500000000001+5−1−51−5−1+5−1−51+5−1+51−500000000000000000000000000000000000000000000
χ9588-8-80000008800008-88-80000-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9688-8-8000000−2+25−2−254ζ12−4ζ28−4ζ12+4ζ28−4ζ4+4ζ364ζ4−4ζ36−2+252−25−2−252+254ζ12−4ζ28−4ζ12+4ζ28−4ζ4+4ζ364ζ4−4ζ362−252+25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9788-8-8000000−2+25−2−25−4ζ12+4ζ284ζ12−4ζ284ζ4−4ζ36−4ζ4+4ζ36−2+252−25−2−252+25−4ζ12+4ζ284ζ12−4ζ284ζ4−4ζ36−4ζ4+4ζ362−252+25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8000000−2−25−2+25−4ζ4+4ζ364ζ4−4ζ36−4ζ12+4ζ284ζ12−4ζ28−2−252+25−2+252−25−4ζ4+4ζ364ζ4−4ζ36−4ζ12+4ζ284ζ12−4ζ282+252−25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8000000−2−25−2+254ζ4−4ζ36−4ζ4+4ζ364ζ12−4ζ28−4ζ12+4ζ28−2−252+25−2+252−254ζ4−4ζ36−4ζ4+4ζ364ζ12−4ζ28−4ζ12+4ζ282+252−25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-8000000880000-88-880000-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8000000−2+25−2−254ζ12−4ζ28−4ζ12+4ζ28−4ζ4+4ζ364ζ4−4ζ362−25−2+252+25−2−25−4ζ12+4ζ284ζ12−4ζ284ζ4−4ζ36−4ζ4+4ζ362−252+25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8000000−2+25−2−25−4ζ12+4ζ284ζ12−4ζ284ζ4−4ζ36−4ζ4+4ζ362−25−2+252+25−2−254ζ12−4ζ28−4ζ12+4ζ28−4ζ4+4ζ364ζ4−4ζ362−252+25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8000000−2−25−2+25−4ζ4+4ζ364ζ4−4ζ36−4ζ12+4ζ284ζ12−4ζ282+25−2−252−25−2+254ζ4−4ζ36−4ζ4+4ζ364ζ12−4ζ28−4ζ12+4ζ282+252−25000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8000000−2−25−2+254ζ4−4ζ36−4ζ4+4ζ364ζ12−4ζ28−4ζ12+4ζ282+25−2−252−25−2+25−4ζ4+4ζ364ζ4−4ζ36−4ζ12+4ζ284ζ12−4ζ282+252−25000000000000000000000000000000000000000000000000000000000000000000000000000000

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