Finite Group Databasebeta

← Group #12016259

Character table — Group #12016259

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size1111222222222222222222444444444444444444444488888888888888888888888888881616161616161616161616161616161616162020202020202020202020204040404040408080
order1244222444558888101020202020881010101010102020202020204040404040404040888816161616404040408080808080808080808080808080808088404040404040404040404040404040402244161616161616161688888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1
χ911-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1iiii−i−i−i−i1111-1-1-1-11-11-1iiii−i−i−i−iii−i−i1-11-1
χ1011-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1iiii−i−i−i−i1111-1-1-1-1-11-11−i−i−i−iiiii−i−iii-11-11
χ1111-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11iiii−i−i−i−i-1-1-1-111111-11-1−i−i−i−iiiiiii−i−i1-1-11
χ1211-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11iiii−i−i−i−i-1-1-1-11111-11-11iiii−i−i−i−i−i−iii-111-1
χ1311-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−i−i−i−iiiii-1-1-1-111111-11-1iiii−i−i−i−i−i−iii1-1-11
χ1411-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−i−i−i−iiiii-1-1-1-11111-11-11−i−i−i−iiiiiii−i−i-111-1
χ1511-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−i−i−i−iiiii1111-1-1-1-11-11-1−i−i−i−iiiii−i−iii1-11-1
χ1611-1-11-1-1-1111111-1-111-1-1-1-11-111-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−i−i−i−iiiii1111-1-1-1-1-11-11iiii−i−i−i−iii−i−i-11-11
χ17222222222222-2-2-2-2222222-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-200000000000000000000000000000000002222000000000000-2-200
χ18222222222222-2-2-2-2222222-2-2222222222222-2-2-2-2-2-2-2-200000000-2-2-2-20000000000000000000000000000000000-2-2-2-20000000000002200
χ192222222222−1+52−1−522222−1+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+52−1−52−1−5222222222−1+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+52−1−52−1−5200000000000000000000
χ202222222222−1+52−1−522222−1+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+52−1−52−1−522222-2-2-2-2−1+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+5200000000000000000000
χ212222222222−1+52−1−522222−1+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+52−1−52−1−52-2-2-2-22222−1+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+5200000000000000000000
χ222222222222−1+52−1−522222−1+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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+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+52−1−52−1−5200000000000000000000
χ232222222222−1−52−1+522222−1−52−1+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+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+5200000000000000000000
χ242222222222−1−52−1+522222−1−52−1+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+522222-2-2-2-2−1−52−1+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+521−521−5200000000000000000000
χ252222222222−1−52−1+522222−1−52−1+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+52-2-2-2-22222−1−52−1+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+521−521−5200000000000000000000
χ262222222222−1−52−1+522222−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1+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+5200000000000000000000
χ272222-22-2-22-222000022222200-2-22-22-2-2-2-2-2220000000000002−22−2000022−2−222−2−222−2−222−2−20000000000000000002-2-2222−2−222−2−200000000
χ282222-22-2-22-222000022222200-2-22-22-2-2-2-2-2220000000000002−22−2000022−2−222−2−222−2−222−2−2000000000000000000-222-2−2−222−2−22200000000
χ292222-22-2-22-222000022222200-2-22-22-2-2-2-2-222000000000000−22−220000−2−222−2−222−2−222−2−2220000000000000000002-2-22−2−222−2−22200000000
χ302222-22-2-22-222000022222200-2-22-22-2-2-2-2-222000000000000−22−220000−2−222−2−222−2−222−2−222000000000000000000-222-222−2−222−2−200000000
χ312222-2-22-2-22222222222222-2-2-2-2-22-22-2-222-2-22222222200000000-2-2-2-200000000000000000000000000000000000000000000002-22-20000
χ322222-2-22-2-22222222222222-2-2-2-2-22-22-2-222-2-22222222200000000-2-2-2-20000000000000000000000000000000000000000000000-22-220000
χ332222-2-22-2-2222-2-2-2-222222222-2-2-22-22-2-222-2-2-2-2-2-2-2-2-2-22-22-2000022220000000000000000002-22-22-22-20000000000000000000000000000
χ342222-2-22-2-2222-2-2-2-222222222-2-2-22-22-2-222-2-2-2-2-2-2-2-2-2-2-22-2200002222000000000000000000-22-22-22-220000000000000000000000000000
χ352222-2-22-2-22−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521+521−52−1+521+52−1−521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+522-22-20000−1+52−1−52−1+52−1−52−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ2800−1+521−52−1−521+52−1+521−52−1−521+52−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ28−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ2800000000000000000000
χ362222-2-22-2-22−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521+521−52−1+521+52−1−521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+522-22-20000−1+52−1−52−1+52−1−52ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ2800−1+521−52−1−521+52−1+521−52−1−521+52ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ28ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ2800000000000000000000
χ372222-2-22-2-22−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521+521−52−1+521+52−1−521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+52-22-220000−1+52−1−52−1+52−1−52−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28001−52−1+521+52−1−521−52−1+521+52−1−52ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ28ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ2800000000000000000000
χ382222-2-22-2-22−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52221−521+521−52−1+521+52−1−521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+52-22-220000−1+52−1−52−1+52−1−52ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ76−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28001−52−1+521+52−1−521−52−1+521+52−1−52−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ28−ζ44+ζ76ζ44−ζ76ζ12−ζ28−ζ12+ζ2800000000000000000000
χ392222-2-22-2-22−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521−521+52−1−521−52−1+521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−522-22-20000−1−52−1+52−1−52−1+52ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ7600−1−521+52−1+521−52−1−521+52−1+521−52ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ76ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ7600000000000000000000
χ402222-2-22-2-22−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521−521+52−1−521−52−1+521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−522-22-20000−1−52−1+52−1−52−1+52−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ7600−1−521+52−1+521−52−1−521+52−1+521−52−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ76−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ7600000000000000000000
χ412222-2-22-2-22−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521−521+52−1−521−52−1+521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−52-22-220000−1−52−1+52−1−52−1+52ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ44+ζ76001+52−1−521−52−1+521+52−1−521−52−1+52−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ76−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ7600000000000000000000
χ422222-2-22-2-22−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52221+521−521+52−1−521−52−1+521+521−52−1−52−1+521+521−521+521+521−521−521+521+521−521−52-22-220000−1−52−1+52−1−52−1+52−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76−ζ12+ζ28ζ12−ζ28−ζ12+ζ28ζ12−ζ28−ζ44+ζ76ζ44−ζ76−ζ44+ζ76ζ44−ζ76001+52−1−521−52−1+521+52−1−521−52−1+52ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ76ζ12−ζ28−ζ12+ζ28ζ44−ζ76−ζ44+ζ7600000000000000000000
χ4322-2-22-2-2-22222-2-22222-2-2-2-2-2222-2-2-2-2-2-22222-2-2-2-2222200000000-2-22200000000000000000000000000000000002-22-2000000000000-2200
χ4422-2-22-2-2-22222-2-22222-2-2-2-2-2222-2-2-2-2-2-22222-2-2-2-2222200000000-2-2220000000000000000000000000000000000-22-220000000000002-200
χ4522-2-22-2-2-222−1+52−1−5222-2-2−1+52−1−521−521−521+521+522-2−1+52−1−521−521−521+521+521−521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+522i2i−2i−2i2i2i−2i−2i−1+52−1−521−521+52−ζ44−ζ76−ζ44−ζ76−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28ζ12+ζ28ζ12+ζ282-2−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28−1+52−1+52−1−52−1−521−521−521+521+5200000000000000000000
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χ1108-8−8i8i000000−2−25−2+25−42424i2−4i22+252−254ζ12+4ζ28−4ζ12−4ζ284ζ44+4ζ76−4ζ44−4ζ7600000000000000−2ζ42−2ζ58+2ζ62+2ζ782ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26−2ζ46+2ζ742ζ42+2ζ58+2ζ62+2ζ78−2ζ42−2ζ58−2ζ62−2ζ782ζ14+2ζ26+2ζ46+2ζ74−2ζ14−2ζ26−2ζ46−2ζ74000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.