Finite Group Databasebeta

← Group #13173369

Character table — Group #13173369

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222224444444444444444444444444444448888888888888888888888888888888888889999181818181818181818182727272727272727363636363636545454545454545454545454
order12442346888812123333336666666121212121212121212121212122424242466666612121212121224242424242424242424242424242424242424242424242488882244882424242416161616161616166612122424161616161616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1iiiiii−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1−i−i−i−i−i−iiiiiii
χ511111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1
χ611111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111
χ711111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i1111-1-1ii−i−i−i−i−i−iiiii
χ811111111-1-1-1-11111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii1111-1-1−i−iiiiiii−i−i−i−i
χ91111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11111111111111-11-1-1-1-1-111-1-1-1-111-1-1
χ101111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111-1-111
χ111111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1iiii−i−i−i−i-11-1111−i−iii−i−iii−i−iii
χ121111-11-1111-1-111111111-1111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1−i−i−i−iiiii-11-1111ii−i−iii−i−iii−i−i
χ131111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11-1-1111111111111-11-11-1-1-1-1-1-111-1-1-1-111
χ141111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11-1-11111-1-1-1-1-1-1-1-1-11-11-1-11111-1-11111-1-1
χ151111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-111-1-1-1-1iiii−i−i−i−i1-11-111−i−i−i−iiiiiii−i−i
χ161111-11-11-1-11111111111-1111111-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-111-1-1-1-1−i−i−i−iiiii1-11-111iiii−i−i−i−i−i−iii
χ1711-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii−i−i1-1-11i−iii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ261-1-11i−iζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46
χ1811-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iii−i−i1-1-11i−iii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ261-1-11i−i−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46
χ1911-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i−i−iii-111-1−ii−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46-111-1−ii−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26
χ2011-1-111-11i−ii−i-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i−i−iii-111-1−ii−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46-111-1−iiζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26
χ2111-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiiiii−i−i-111-1i−iii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26-111-1i−iζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46
χ2211-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiiiii−i−i-111-1i−iii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26-111-1i−i−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46
χ2311-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−iii1-1-11−ii−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ461-1-11−ii−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26
χ2411-1-111-11−ii−ii-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii−i−iii1-1-11−ii−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ461-1-11−iiζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26
χ2511-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i11-1-1−iiii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ2611-1-1−ii−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46
χ2611-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i11-1-1−iiii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ2611-1-1−iiζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46
χ2711-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii−i−iii-1-111i−i−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46-1-111i−iζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26
χ2811-1-1-1111i−i−ii-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii−i−iii-1-111i−i−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46-1-111i−i−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26
χ2911-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−iii−i−i-1-111−iiii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26-1-111−ii−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46
χ3011-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−iii−i−i-1-111−iiii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26-1-111−iiζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46
χ3111-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iii11-1-1i−i−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ4611-1-1i−iζ10+ζ26−ζ10−ζ26ζ14+ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ10−ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26
χ3211-1-1-1111−iii−i-1-1111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1−iii−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iii11-1-1i−i−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ4611-1-1i−i−ζ10−ζ26ζ10+ζ26−ζ14−ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46ζ14+ζ46−ζ14−ζ46ζ10+ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26
χ3322222-12-12222-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222222222-1-1-1-100000000-1-1-1-1-1-1000000000000
χ3422222-12-12222-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-2-2111100000000111111000000000000
χ3522222-12-1-2-2-2-2-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-211112222-2-2-2-222-1-1-1-1000000001111-1-1000000000000
χ3622222-12-1-2-2-2-2-1-122-1-1-1-1-122-1-1-1-1-12222-1-1-1-1-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-21111-2-21111-2-2-2-22222-2-2111100000000-1-1-1-111000000000000
χ372222-2-1-2-122-2-2-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-1-1-111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-2111122222-22-2-2-2-1-1-1-100000000-11-1111000000000000
χ382222-2-1-2-122-2-2-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-1-1-111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-2-22-22221111000000001-11-1-1-1000000000000
χ392222-2-1-2-1-2-222-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-111-1-1-2-21111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-12222-22-22-2-2-1-1-1-1000000001-11-111000000000000
χ402222-2-1-2-1-2-222-1-122-1-1-1-1122-1-1-1-112222-1-1-1-1-1-1-1-111-1-1-2-21111-2-21111-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-22-22-222111100000000-11-11-1-1000000000000
χ4122-2-22-1-2-12i−2i2i−2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111−ii−ii22-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−2i−2i2-2-222i−2i−i−iii00000000-111-1−ii000000000000
χ4222-2-22-1-2-12i−2i2i−2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111−ii−ii22-1-1-1-1-2-211112i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii−2i−2i2i2i-222-2−2i2iii−i−i000000001-1-11i−i000000000000
χ4322-2-22-1-2-1−2i2i−2i2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111i−ii−i22-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i2i2i−2i−2i-222-22i−2i−i−iii000000001-1-11−ii000000000000
χ4422-2-22-1-2-1−2i2i−2i2i1122-1-1-1-1-122-1-1-1-11-2-2-2-211111111i−ii−i22-1-1-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2i2i2i2-2-22−2i2iii−i−i00000000-111-1i−i000000000000
χ4522-2-2-2-12-12i−2i−2i2i1122-1-1-1-1122-1-1-1-1-1-2-2-2-211111111−iii−i-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i2i2i−2i−2i22-2-2−2i2i−i−iii00000000-1-111i−i000000000000
χ4622-2-2-2-12-12i−2i−2i2i1122-1-1-1-1122-1-1-1-1-1-2-2-2-211111111−iii−i-2-2111122-1-1-1-12i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i−2i−2i2i2i-2-2222i−2iii−i−i0000000011-1-1−ii000000000000
χ4722-2-2-2-12-1−2i2i2i−2i1122-1-1-1-1122-1-1-1-1-1-2-2-2-211111111i−i−ii-2-2111122-1-1-1-1−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii2i2i−2i−2i-2-222−2i2i−i−iii0000000011-1-1i−i000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.