Finite Group Databasebeta

← Group #11995680

Character table — Group #11995680

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107
size1111222222222222222244444444444444444444444444488888888888888888888881616161616161616161616161616161616161616202020204040404040404040404040404040
order1222224444445510101010101044488881010101020202020202020202020202020202020882020202040404040404040404040404040404040448820202020202020204040404040404040224424888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ91111111-1-1-11-1111111111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i1111-1-1-1-1iiii−i−i−i−i11-1-11-111-1-1ii−i−iii−i−i
χ101111111-1-1-11-1111111111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i1111-1-1-1-1iiii−i−i−i−i-1-111-11-1-111−i−iii−i−iii
χ111111111-1-1-11-1111111111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-1-1-11111−i−i−i−iiiii11-1-11-1-1-111ii−i−i−i−iii
χ121111111-1-1-11-1111111111-1-1ii−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-1-1-11111−i−i−i−iiiii-1-111-1111-1-1−i−iiiii−i−i
χ131111111-1-1-11-1111111111-1-1−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii1111-1-1-1-1−i−i−i−iiiii11-1-11-111-1-1−i−iii−i−iii
χ141111111-1-1-11-1111111111-1-1−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii1111-1-1-1-1−i−i−i−iiiii-1-111-11-1-111ii−i−iii−i−i
χ151111111-1-1-11-1111111111-1-1−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-1-1-11111iiii−i−i−i−i11-1-11-1-1-111−i−iiiii−i−i
χ161111111-1-1-11-1111111111-1-1−i−iii11111111-1-1-1-1-1-1-1-1-1-1-1-1−ii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-1-1-11111iiii−i−i−i−i-1-111-1111-1-1ii−i−i−i−iii
χ17222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222−1+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+52−1−5222−1+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+52−1−52−1−52−1−52−1−522222−1+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+52−1−52−1−52000000000000000000
χ18222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222−1+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+52−1−5222−1+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+52−1−52−1−52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000
χ19222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000000
χ20222222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52222-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-2-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ21222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222−1−52−1−52−1+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+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+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+52000000000000000000
χ22222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222−1−52−1−52−1+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+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+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000000
χ23222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000000
χ24222222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52-2-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ252222222-2-2-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-22i2i−2i−2i−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+522i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ142-22i−2i−1+52−1+52−1−52−1−521−521−521+521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000000000000000
χ262222222-2-2-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-22i2i−2i−2i−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+522i−2i−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14-22−2i2i1−521−521+521+52−1+52−1+52−1−52−1−52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000000000000000
χ272222222-2-2-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-2−2i−2i2i2i−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+52−2i2i−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ142-2−2i2i−1+52−1+52−1−52−1−521−521−521+521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14000000000000000000
χ282222222-2-2-22-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522-2-2−2i−2i2i2i−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+52−2i2i−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14-222i−2i1−521−521+521+52−1+52−1+52−1−52−1−52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14000000000000000000
χ292222222-2-2-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-22i2i−2i−2i−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+521−522i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ382-22i−2i−1−52−1−52−1+52−1+521+521+521−521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000000000000000
χ302222222-2-2-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-22i2i−2i−2i−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+521−522i−2i−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38-22−2i2i1+521+521−521−52−1−52−1−52−1+52−1+52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000000000000000
χ312222222-2-2-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-2−2i−2i2i2i−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+521−52−2i2i−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ382-2−2i2i−1−52−1−52−1+52−1+521+521+521−521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38000000000000000000
χ322222222-2-2-22-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522-2-2−2i−2i2i2i−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+521−52−2i2i−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38−ζ22−ζ38-222i−2i1+521+521−521−52−1−52−1−52−1+52−1+52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38000000000000000000
χ33222222-2222-2222222222-2-2-222222222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000000000000000
χ34222222-2222-2222222222-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-222-2-222-2-222-2-22200000000000000000000000000000000000000
χ35222222-2222-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-22222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521+521−521+52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+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−ζ36000000000000000000
χ36222222-2222-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-22222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52-2-21−521+521−521+52−1+52−1+521−521−52−1−52−1−521+521+52−1+52−1+521−521−52−1−52−1−521+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+ζ36000000000000000000
χ37222222-2222-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52221−521+521−521+521−521−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+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+ζ36000000000000000000
χ38222222-2222-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52221−521+521−521+521−521−52−1+52−1+521+521+52−1−52−1−521−521−52−1+52−1+521+521+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−ζ36000000000000000000
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χ974-4-44-440-4-4404−1−5−1+5−1−51+5−1+51−51+51−500000001+5−1−51−5−1+500001+51−50000−1−51+5−1+51−5−1−5−1+5000000002ζ6−2ζ14−2ζ6+2ζ1400−2ζ22+2ζ382ζ22−2ζ3800−2ζ6+2ζ142ζ6−2ζ14002ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000000000000000
χ984-4-44-440-4-4404−1−5−1+5−1−51+5−1+51−51+51−500000001+5−1−51−5−1+500001+51−50000−1−51+5−1+51−5−1−5−1+500000000−2ζ6+2ζ142ζ6−2ζ14002ζ22−2ζ38−2ζ22+2ζ38002ζ6−2ζ14−2ζ6+2ζ1400−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000000000000000
χ9988-8-8008000-80−2+25−2−252−25−2+252+25−2−252−252+2500000000000−2+252−25−2−252+25000000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8008000-80−2−25−2+252+25−2−252−25−2+252+252−2500000000000−2−252+25−2+252−25000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-800-800080−2+25−2−252−25−2+252+25−2−252−252+25000000000002−25−2+252+25−2−25000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-800-800080−2−25−2+252+25−2−252−25−2+252+252−25000000000002+25−2−252−25−2+25000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-80000000088-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-800000000−2+25−2−252−252−252+252+25−2+25−2−25000000000000000004ζ12−4ζ28−4ζ12+4ζ28−4ζ4+4ζ364ζ4−4ζ36000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-800000000−2+25−2−252−252−252+252+25−2+25−2−2500000000000000000−4ζ12+4ζ284ζ12−4ζ284ζ4−4ζ36−4ζ4+4ζ36000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-800000000−2−25−2+252+252+252−252−25−2−25−2+2500000000000000000−4ζ4+4ζ364ζ4−4ζ36−4ζ12+4ζ284ζ12−4ζ28000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-800000000−2−25−2+252+252+252−252−25−2−25−2+25000000000000000004ζ4−4ζ36−4ζ4+4ζ364ζ12−4ζ28−4ζ12+4ζ28000000000000000000000000000000000000000000000000000000000000000000

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