Finite Group Databasebeta

← Group #13138769

Character table — Group #13138769

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size111111112222222222222222222266666666666666669999999912121212121212121212121212121212121212121212121218181818181818181818181818181818181818181818181818181818181818181818181836363636363636363636363636363636
order122244443666888812121212242424242424242433666666121212121212121244444444366612121212242424242424242424242424242424242244444488888888888812121212121212122424242424242424661212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ5111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ8111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ91111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-111-1-111−i−iiiii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ111111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii−i−iii-1-1-1-11111−i−i−i−iiiii11-1-111-1-1−i−iiiii−i−i
χ121111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-1-11111-1-1−i−iii−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111ii−i−i−i−iii
χ131111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ141111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-111-1-111ii−i−i−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ151111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i11-1-111-1-1ii−i−i−i−iii
χ161111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i-1-111-1-111−i−iiiii−i−i
χ1711-1-111-1-111-1-11-11-111-1-111-1-111-1-111-1-11-1-11-1-111-1-111ii−i−iii−i−i1-1-11-1-1111-11-11-11-111-1-111-1-11-11-1i−ii−i1-11-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i1-1i−ii−i1-1i−ii−i1-11-1
χ1811-1-111-1-111-1-11-11-111-1-111-1-111-1-111-1-11-1-11-1-111-1-111ii−i−iii−i−i1-1-11-1-1111-11-11-11-111-1-111-1-1-11-11−ii−ii-11-11i−ii−i−ii−iiii−i−iii−i−iii−i−iii−i−i-11−ii−ii-11−ii−ii-11-11
χ1911-1-111-1-111-1-11-11-111-1-111-1-111-1-111-1-11-1-11-1-111-1-111−i−iii−i−iii1-1-11-1-1111-11-11-11-111-1-111-1-11-11-1−ii−ii1-11-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii1-1−ii−ii1-1−ii−ii1-11-1
χ2011-1-111-1-111-1-11-11-111-1-111-1-111-1-111-1-11-1-11-1-111-1-111−i−iii−i−iii1-1-11-1-1111-11-11-11-111-1-111-1-1-11-11i−ii−i-11-11−ii−iii−ii−i−i−iii−i−iii−i−iii−i−iii-11i−ii−i-11i−ii−i-11-11
χ2111-1-111-1-111-1-1-11-1111-1-1-1-111-1-11111-1-11-1-11-1-111-1-111ii−i−iii−i−i1-1-11-1-111-11-11-11-11-1-111-1-1111-11-1i−ii−i-11-11−ii−ii−ii−iiii−i−iii−i−i−i−iii−i−iii1-1i−ii−i1-1−ii−ii-11-11
χ2211-1-111-1-111-1-1-11-1111-1-1-1-111-1-11111-1-11-1-11-1-111-1-111ii−i−iii−i−i1-1-11-1-111-11-11-11-11-1-111-1-111-11-11−ii−ii1-11-1−ii−iii−ii−iii−i−iii−i−i−i−iii−i−iii-11−ii−ii-11i−ii−i1-11-1
χ2311-1-111-1-111-1-1-11-1111-1-1-1-111-1-11111-1-11-1-11-1-111-1-111−i−iii−i−iii1-1-11-1-111-11-11-11-11-1-111-1-1111-11-1−ii−ii-11-11i−ii−ii−ii−i−i−iii−i−iiiii−i−iii−i−i1-1−ii−ii1-1i−ii−i-11-11
χ2411-1-111-1-111-1-1-11-1111-1-1-1-111-1-11111-1-11-1-11-1-111-1-111−i−iii−i−iii1-1-11-1-111-11-11-11-11-1-111-1-111-11-11i−ii−i1-11-1i−ii−i−ii−ii−i−iii−i−iiiii−i−iii−i−i-11i−ii−i-11−ii−ii1-11-1
χ2511-1-1-1-11111-1-1i−i−ii-1-111ii−i−i−i−iii11-1-11-1-1111-1-111-1-1ii−i−i−i−iii1-1-1111-1-1i−i−iii−i−iiii−i−i−i−iii1-1-11i−i−iii−i−ii-111-1-111-1ii−i−i−i−iii-1-11111-1-11-1i−i−ii-11-111-1i−i−ii
χ2611-1-1-1-11111-1-1i−i−ii-1-111ii−i−i−i−iii11-1-11-1-1111-1-111-1-1ii−i−i−i−iii1-1-1111-1-1i−i−iii−i−iiii−i−i−i−iii-111-1−iii−i−iii−i-111-11-1-11ii−i−i−i−iii-1-11111-1-1-11−iii−i1-11-1-11−iii−i
χ2711-1-1-1-11111-1-1i−i−ii-1-111ii−i−i−i−iii11-1-11-1-1111-1-111-1-1−i−iiiii−i−i1-1-1111-1-1i−i−iii−i−iiii−i−i−i−iii1-1-11−iii−ii−i−ii1-1-111-1-11−i−iiiii−i−i11-1-1-1-1111-1−iii−i-111-1-11i−i−ii
χ2811-1-1-1-11111-1-1i−i−ii-1-111ii−i−i−i−iii11-1-11-1-1111-1-111-1-1−i−iiiii−i−i1-1-1111-1-1i−i−iii−i−iiii−i−i−i−iii-111-1i−i−ii−iii−i1-1-11-111-1−i−iiiii−i−i11-1-1-1-111-11i−i−ii1-1-111-1−iii−i
χ2911-1-1-1-11111-1-1−iii−i-1-111−i−iiiii−i−i11-1-11-1-1111-1-111-1-1ii−i−i−i−iii1-1-1111-1-1−iii−i−iii−i−i−iiiii−i−i1-1-11i−i−ii−iii−i1-1-111-1-11ii−i−i−i−iii11-1-1-1-1111-1i−i−ii-111-1-11−iii−i
χ3011-1-1-1-11111-1-1−iii−i-1-111−i−iiiii−i−i11-1-11-1-1111-1-111-1-1ii−i−i−i−iii1-1-1111-1-1−iii−i−iii−i−i−iiiii−i−i-111-1−iii−ii−i−ii1-1-11-111-1ii−i−i−i−iii11-1-1-1-111-11−iii−i1-1-111-1i−i−ii
χ3111-1-1-1-11111-1-1−iii−i-1-111−i−iiiii−i−i11-1-11-1-1111-1-111-1-1−i−iiiii−i−i1-1-1111-1-1−iii−i−iii−i−i−iiiii−i−i1-1-11−iii−i−iii−i-111-1-111-1−i−iiiii−i−i-1-11111-1-11-1−iii−i-11-111-1−iii−i
χ3211-1-1-1-11111-1-1−iii−i-1-111−i−iiiii−i−i11-1-11-1-1111-1-111-1-1−i−iiiii−i−i1-1-1111-1-1−iii−i−iii−i−i−iiiii−i−i-111-1i−i−iii−i−ii-111-11-1-11−i−iiiii−i−i-1-11111-1-1-11i−i−ii1-11-1-11i−i−ii
χ3322222222222222222222222222222-1-1-1222-1-1-12222-1-100000000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200002222000000000000000000000000-1-10000-1-10000-1-1-1-1
χ3422222222222222222222222222222-1-1-1222-1-1-12222-1-100000000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-20000000000000000000000001100001100001111
χ352222222222222222222222222222-1222-1-1-1222-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002222000000002222000000000000000000-1-1-1-100-1-1-1-10000
χ362222222222222222222222222222-1222-1-1-1222-1-1-1-12200000000-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-200000000-2-2-2-200000000000000000011110011110000
χ37222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1222-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-2-2-2-211111111111122220000-2-2-2-2000000000000000000000000-1-10000-1-100001111
χ38222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1222-1-1-12222-1-100000000-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-200002222000000000000000000000000110000110000-1-1-1-1
χ39222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1222-1-1-1222-1-1-1-12200000000-1-1-1-1-1-1-1-11111-2-2-2-2111111110000222200000000-2-2-2-2000000000000000000-1-1-1-10011110000
χ40222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1222-1-1-1222-1-1-1-12200000000-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-2-2-2000000002222000000000000000000111100-1-1-1-10000
χ412222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i2-1-1-1222-111-2-2-2-21100000000-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii22-2-200002i2i−2i−2i000000000000000000000000-1-10000110000−i−iii
χ422222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i2-1-1-1222-111-2-2-2-21100000000-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii-2-2220000−2i−2i2i2i000000000000000000000000110000-1-10000ii−i−i
χ432222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-1222-1-1-12-2-21111-2-200000000-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii000022-2-2000000002i2i−2i−2i000000000000000000-1-11100−i−iii0000
χ442222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-1222-1-1-12-2-21111-2-200000000-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000-2-22200000000−2i−2i2i2i00000000000000000011-1-100ii−i−i0000
χ452222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-1-1-1222-111-2-2-2-21100000000-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i22-2-20000−2i−2i2i2i000000000000000000000000-1-10000110000ii−i−i
χ462222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-1-1-1222-111-2-2-2-21100000000-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i-2-22200002i2i−2i−2i000000000000000000000000110000-1-10000−i−iii
χ472222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i-1222-1-1-12-2-21111-2-200000000-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i000022-2-200000000−2i−2i2i2i000000000000000000-1-11100ii−i−i0000
χ482222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i-1222-1-1-12-2-21111-2-200000000-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000-2-222000000002i2i−2i−2i00000000000000000011-1-100−i−iii0000
χ4922-2-222-2-222-2-22-22-222-2-222-2-222-2-22-1112-2-2-11122-2-2-1-100000000-111-111-1-12-22-2-11-11-1-111-1-1112-22-200002-22-2000000000000000000000000-110000-110000-11-11
χ5022-2-222-2-222-2-22-22-222-2-222-2-222-2-22-1112-2-2-11122-2-2-1-100000000-111-111-1-12-22-2-11-11-1-111-1-111-22-220000-22-220000000000000000000000001-100001-100001-11-1
χ5122-2-222-2-222-2-22-22-222-2-222-2-222-2-2-12-2-2-1112-2-2-1-1112200000000-111-111-1-1-11-112-22-2-1-111-1-11100002i−2i2i−2i000000002i−2i2i−2i000000000000000000−ii−ii00−ii−ii0000
χ5222-2-222-2-222-2-22-22-222-2-222-2-222-2-2-12-2-2-1112-2-2-1-1112200000000-111-111-1-1-11-112-22-2-1-111-1-1110000−2i2i−2i2i00000000−2i2i−2i2i000000000000000000i−ii−i00i−ii−i0000
χ5322-2-222-2-222-2-2-22-2222-2-2-2-222-2-2222-1112-2-2-11122-2-2-1-100000000-111-111-1-1-22-221-11-111-1-111-1-12-22-20000-22-22000000000000000000000000-110000-1100001-11-1
χ5422-2-222-2-222-2-2-22-2222-2-2-2-222-2-2222-1112-2-2-11122-2-2-1-100000000-111-111-1-1-22-221-11-111-1-111-1-1-22-2200002-22-20000000000000000000000001-100001-10000-11-11
χ5522-2-222-2-222-2-2-22-2222-2-2-2-222-2-222-12-2-2-1112-2-2-1-1112200000000-111-111-1-11-11-1-22-2211-1-111-1-100002i−2i2i−2i00000000−2i2i−2i2i000000000000000000−ii−ii00i−ii−i0000
χ5622-2-222-2-222-2-2-22-2222-2-2-2-222-2-222-12-2-2-1112-2-2-1-1112200000000-111-111-1-11-11-1-22-2211-1-111-1-10000−2i2i−2i2i000000002i−2i2i−2i000000000000000000i−ii−i00−ii−ii0000
χ5722-2-2-2-22222-2-22i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i2-1112-2-2-1-1-1-2-2221100000000-111-1-1-1112i−2i−2i2i−iii−i−i−iiiii−i−i2-2-2200002i−2i−2i2i000000000000000000000000-1100001-10000−iii−i
χ5822-2-2-2-22222-2-22i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i2-1112-2-2-1-1-1-2-2221100000000-111-1-1-1112i−2i−2i2i−iii−i−i−iiiii−i−i-222-20000−2i2i2i−2i0000000000000000000000001-10000-110000i−i−ii
χ5922-2-2-2-22222-2-22i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i-12-2-2-11122211-1-1-2-200000000-111-1-1-111−iii−i2i−2i−2i2i−i−iiiii−i−i00002i−2i−2i2i00000000-222-2000000000000000000−iii−i001-1-110000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.