Finite Group Databasebeta

← Group #12015824

Character table — Group #12015824

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111122222222222222444444444444444444444444888888888888888888888888888816161616161616161616161616161616161620202020404040404040404040408080
order124422244455101020202020888810101010101020202020202040404040404040408888161616164040404080808080808080808080808080808080884040404040404040404040404040404022448888881616161688
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111ii−i−i11-1-111-1-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i1-111-1-1i−i
χ1011-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111ii−i−i11-1-111-1-111111111-1-1-1-1-1-1-1-1i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−i−iii-11-1-111−ii
χ1111-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111ii−i−i-1-11111-1-1-1-1-1-1-1-1-1-111111111−iiiiii−i−i−i−i−i−i−i−iiiii1-11-1ii−i−i1-1-1-111−ii
χ1211-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111ii−i−i-1-11111-1-1-1-1-1-1-1-1-1-111111111−iiiiii−i−i−i−i−i−i−i−iiiii-11-11−i−iii-1111-1-1i−i
χ1311-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111−i−iii11-1-111-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii1-111-1-1−ii
χ1411-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111−i−iii11-1-111-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−iiiii−i−i−i−iiiii-11-11ii−i−i-11-1-111i−i
χ1511-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111−i−iii-1-11111-1-1-1-1-1-1-1-1-1-111111111i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1−i−iii1-1-1-111i−i
χ1611-1-11-1-111-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111−i−iii-1-11111-1-1-1-1-1-1-1-1-1-111111111i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i-1111-1-1−ii
χ17222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2000000000000000000000000000000000022220000-2-2000000
χ18222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000000000-2-2-2-2000022000000
χ192222222222−1+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+52−1−52−1−5222222222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+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+52−1−52−1−520000000000000000
χ202222222222−1+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+52−1−52−1−522222-2-2-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000
χ212222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222−1+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+52−1−52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+520000000000000000
χ222222222222−1+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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000
χ232222222222−1−52−1+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+5222222222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+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+520000000000000000
χ242222222222−1−52−1+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+522222-2-2-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52-2-2−1−52−1−52−1+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+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+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−520000000000000000
χ262222222222−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000
χ2722222-2-2-2-2222222222000022-2-2-2-2-2-222-2-20000000000002−22−2000022−2−222−2−222−2−222−2−20000000000000000002-2-220000002−22−200
χ2822222-2-2-2-2222222222000022-2-2-2-2-2-222-2-20000000000002−22−2000022−2−222−2−222−2−222−2−2000000000000000000-222-2000000−22−2200
χ2922222-2-2-2-2222222222000022-2-2-2-2-2-222-2-2000000000000−22−220000−2−222−2−222−2−222−2−2220000000000000000002-2-22000000−22−2200
χ3022222-2-2-2-2222222222000022-2-2-2-2-2-222-2-2000000000000−22−220000−2−222−2−222−2−222−2−222000000000000000000-222-20000002−22−200
χ312222-22-2-22-2222222222-22-2-2-22-22-2-2-2-2-222222222222-22-20000-2-2-2-20000000000000000002-22-22-22-2000000000000000000000000
χ322222-22-2-22-2222222222-22-2-2-22-22-2-2-2-2-22222222222-22-220000-2-2-2-2000000000000000000-22-22-22-22000000000000000000000000
χ332222-22-2-22-222222222-22-22-2-22-22-2-2-2-2-222-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000002-22-200000000
χ342222-22-2-22-222222222-22-22-2-22-22-2-2-2-2-222-2-2-2-2-2-2-2-200000000222200000000000000000000000000000000000000-22-2200000000
χ352222-22-2-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-21−521+52−1+521−52−1−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-22-200001−521+521−521+52ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ3600−1+521−52−1−521+52−1+521−52−1−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ362222-22-2-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-21−521+52−1+521−52−1−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-22-200001−521+521−521+52−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ3600−1+521−52−1−521+52−1+521−52−1−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ372222-22-2-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-21−521+52−1+521−52−1−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22-2200001−521+521−521+52ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ36001−52−1+521+52−1−521−52−1+521+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000000000000
χ382222-22-2-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-22-21−521+52−1+521−52−1−521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22-2200001−521+521−521+52−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ36001−52−1+521+52−1−521−52−1+521+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000000000000
χ392222-22-2-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-21+521−52−1−521+52−1+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+522-22-200001+521−521+521−52−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ2800−1−521+52−1+521−52−1−521+52−1+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000000000000
χ402222-22-2-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-21+521−52−1−521+52−1+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+522-22-200001+521−521+521−52ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ2800−1−521+52−1+521−52−1−521+52−1+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
χ412222-22-2-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-21+521−52−1−521+52−1+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+52-22-2200001+521−521+521−52−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28001+52−1−521−52−1+521+52−1−521−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000000000000
χ422222-22-2-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-22-21+521−52−1−521+52−1+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+52-22-2200001+521−521+521−52ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28001+52−1−521−52−1+521+52−1−521−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000000000000
χ4322-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-20000000000002−2−22000022−2−222−2−2−2−222−2−22200000000000000000022-2-20000002−2−2200
χ4422-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-20000000000002−2−22000022−2−222−2−2−2−222−2−222000000000000000000-2-222000000−222−200
χ4522-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-2000000000000−222−20000−2−222−2−22222−2−222−2−200000000000000000022-2-2000000−222−200
χ4622-2-2222-2-2-22222-2-2-2-20000222222-2-2-2-2-2-2000000000000−222−20000−2−222−2−22222−2−222−2−2000000000000000000-2-2220000002−2−2200
χ4722-2-22-2-222-22222-2-2-2-222-2-222-2-2-2-222-2-2222222-2-2-2-200000000-2-22200000000000000000000000000000000002-22-20000-22000000
χ4822-2-22-2-222-22222-2-2-2-222-2-222-2-2-2-222-2-2222222-2-2-2-200000000-2-2220000000000000000000000000000000000-22-2200002-2000000
χ4922-2-22-2-222-2−1+52−1−52−1+52−1−521−521−521+521+52-2-222−1+52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−522i2i−2i−2i22-2-2−1+52−1−521−521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+522i−2i−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.