Finite Group Databasebeta

← Group #13135086

Character table — Group #13135086

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222222222222222226666666666666666121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order12448888234666881212121224242424242424243366121212122424242424242424366666121212121212242424242424242424242424161616161616161648484848484848484848484848484848246688121216161616242424244848484848484848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ51111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-111ii−i−i-1-1-1-1iiii−i−i−i−i
χ61111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-1-1−i−iii1111−i−i−i−iiiii
χ71111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-111−i−iii-1-1-1-1−i−i−i−iiiii
χ81111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-1-1ii−i−i1111iiii−i−i−i−i
χ911-1-1ii−i−i-111-1-11i−i11-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1-1-1-111111-1-1i−ii−iiiii−i−i−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ261-111i−i-1-1ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26ii−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ1011-1-1ii−i−i-111-1-11i−i11-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1-1-1-111111-1-1i−ii−iiiii−i−i−i−iζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26-11-1-1−ii11−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26−i−iii−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ1111-1-1ii−i−i-111-1-11i−i11-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1-1-1-111111-1-1i−ii−iiiii−i−i−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ261-111i−i-1-1−ζ14−ζ46ζ14+ζ46ζ10+ζ26−ζ10−ζ26ii−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ1211-1-1ii−i−i-111-1-11i−i11-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1-1-1-111111-1-1i−ii−iiiii−i−i−i−i−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26-11-1-1−ii11ζ14+ζ46−ζ14−ζ46−ζ10−ζ26ζ10+ζ26−i−iiiζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ1311-1-1−i−iii-111-1-11−ii11-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1-1-1-111111-1-1−ii−ii−i−i−i−iiiii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ461-111−ii-1-1−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46−i−iii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46
χ1411-1-1−i−iii-111-1-11−ii11-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1-1-1-111111-1-1−ii−ii−i−i−i−iiiii−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46-11-1-1i−i11ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46ii−i−iζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46
χ1511-1-1−i−iii-111-1-11−ii11-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1-1-1-111111-1-1−ii−ii−i−i−i−iiiiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ461-111−ii-1-1ζ10+ζ26−ζ10−ζ26−ζ14−ζ46ζ14+ζ46−i−iiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46
χ1611-1-1−i−iii-111-1-11−ii11-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1-1-1-111111-1-1−ii−ii−i−i−i−iiiiiζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ10−ζ26−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46ζ14+ζ46-11-1-1i−i11−ζ10−ζ26ζ10+ζ26ζ14+ζ46−ζ14−ζ46ii−i−i−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46
χ1722222222222222222222222222222-12-122-1-1-1-1-1-12222-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-122-1-10000-1-1-1-100000000
χ1822222222222222222222222222222-12-122-1-1-1-1-1-12222-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-211-2-2110000111100000000
χ192222222222222222222222222222-12-12-1-1222222-1-1-1-1-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000000000000000022220000-1-1-1-1-1-1-1-1
χ202222222222222222222222222222-12-12-1-1222222-1-1-1-1-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000000000000000000000-2-2-2-2000011111111
χ2122222222-22-2-2-22-2-2-2-2222222-2-2-2-222222222222222222-2-2-2-22-2-2-2-222-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ2222222222-22-2-2-22-2-2-2-2222222-2-2-2-22-12-122-1-1-1-1-1-12222-1-2111-1-2111-1-1-2-211-1-111-1-11100000000000000000000000000−i3i300−i3i30000−i3i3−i3i300000000
χ2322222222-22-2-2-22-2-2-2-2222222-2-2-2-22-12-122-1-1-1-1-1-12222-1-2111-1-2111-1-1-2-211-1-111-1-11100000000000000000000000000i3−i300i3−i30000i3−i3i3−i300000000
χ2422222222-22-2-2-22-2-2-2-2222222-2-2-2-2-12-12-1-1222222-1-1-1-1-11-211-11-211-1-111-2-2-1-111-1-1110000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ2522222222-22-2-2-22-2-2-2-2222222-2-2-2-2-12-12-1-1222222-1-1-1-1-11-211-11-211-1-111-2-2-1-111-1-1110000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ262222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-22-12-122-1-11111-2-2-2-2-12-1-1-1-12-1-1-1-1-1-2-2111111111100000000000000000000000022-1-1-2-2-1-10000111100000000
χ272222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-22-12-122-1-11111-2-2-2-2-12-1-1-1-12-1-1-1-1-1-2-21111111111000000000000000000000000-2-21122110000-1-1-1-100000000
χ282222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2-12-12-1-122-2-2-2-21111-1-12-1-1-1-12-1-1-1-111-2-211111111000000000000000000000000000000002i2i−2i−2i0000−i−i−i−iiiii
χ292222-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2-12-12-1-122-2-2-2-21111-1-12-1-1-1-12-1-1-1-111-2-21111111100000000000000000000000000000000−2i−2i2i2i0000iiii−i−i−i−i
χ302222-2-2-2-2-22-2-2-2222-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-22-2-2-2-22-2-2-2-2222222-2-222-2-222000000000000000000000000000000000000000000000000
χ312222-2-2-2-2-22-2-2-2222-2-222-2-2-2-222222-12-122-1-11111-2-2-2-2-1-2111-1-2111-1-122-1-111-1-111-1-100000000000000000000000000−i3i300−i3i30000i3−i3i3−i300000000
χ322222-2-2-2-2-22-2-2-2222-2-222-2-2-2-222222-12-122-1-11111-2-2-2-2-1-2111-1-2111-1-122-1-111-1-111-1-100000000000000000000000000i3−i300i3−i30000−i3i3−i3i300000000
χ332222-2-2-2-2-22-2-2-2222-2-222-2-2-2-22222-12-12-1-122-2-2-2-21111-11-211-11-211-1-1-1-12211-1-111-1-100000000000000000000000000000000000000003−33−3−33−33
χ342222-2-2-2-2-22-2-2-2222-2-222-2-2-2-22222-12-12-1-122-2-2-2-21111-11-211-11-211-1-1-1-12211-1-111-1-10000000000000000000000000000000000000000−33−333−33−3
χ3522-2-22i2i−2i−2i22-2222−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i2222-2-2-2-22i2i−2i−2i2i2i−2i−2i222222-2-2-2-2-2-2−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3622-2-22i2i−2i−2i22-2222−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i2-12-1-2-211−i−iii2i2i−2i−2i-12-1-1-1-1-211111−2i2ii−i−i−iiiii−i−i00000000000000000000000000−i3i300i3−i300003−3−3300000000
χ3722-2-22i2i−2i−2i22-2222−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i2-12-1-2-211−i−iii2i2i−2i−2i-12-1-1-1-1-211111−2i2ii−i−i−iiiii−i−i00000000000000000000000000i3−i300−i3i30000−333−300000000
χ3822-2-22i2i−2i−2i22-2222−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i-12-1211-2-22i2i−2i−2i−i−iii-1-12-1-1-11-21111i−i−2i2i−i−iiiii−i−i0000000000000000000000000000000000000000−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26
χ3922-2-22i2i−2i−2i22-2222−2i2i-2-2-2-22i2i−2i−2i−2i−2i2i2i-12-1211-2-22i2i−2i−2i−i−iii-1-12-1-1-11-21111i−i−2i2i−i−iiiii−i−i0000000000000000000000000000000000000000ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26
χ4022-2-22i2i−2i−2i-222-2-222i−2i22-2-22i2i−2i−2i2i2i−2i−2i2-12-1-2-211−i−iii2i2i−2i−2i-1-2111-12-1-1-1112i−2i−ii−i−i−i−iiiii0000000000000000000000002-2-1-12i−2i110000−i−iii00000000
χ4122-2-22i2i−2i−2i-222-2-222i−2i22-2-22i2i−2i−2i2i2i−2i−2i2-12-1-2-211−i−iii2i2i−2i−2i-1-2111-12-1-1-1112i−2i−ii−i−i−i−iiiii000000000000000000000000-2211−2i2i-1-10000ii−i−i00000000
χ4222-2-22i2i−2i−2i-222-2-222i−2i22-2-22i2i−2i−2i2i2i−2i−2i-12-1211-2-22i2i−2i−2i−i−iii-11-211-1-12-1-111−ii2i−2i−i−i−i−iiiii000000000000000000000000000000002ζ14+2ζ46−2ζ14−2ζ46−2ζ10−2ζ262ζ10+2ζ260000−ζ14−ζ46−ζ14−ζ46ζ14+ζ46ζ14+ζ46ζ10+ζ26ζ10+ζ26−ζ10−ζ26−ζ10−ζ26
χ4322-2-22i2i−2i−2i-222-2-222i−2i22-2-22i2i−2i−2i2i2i−2i−2i-12-1211-2-22i2i−2i−2i−i−iii-11-211-1-12-1-111−ii2i−2i−i−i−i−iiiii00000000000000000000000000000000−2ζ14−2ζ462ζ14+2ζ462ζ10+2ζ26−2ζ10−2ζ260000ζ14+ζ46ζ14+ζ46−ζ14−ζ46−ζ14−ζ46−ζ10−ζ26−ζ10−ζ26ζ10+ζ26ζ10+ζ26
χ4422-2-2−2i−2i2i2i22-22222i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i222222-2-2-2-2-2-22i−2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4522-2-2−2i−2i2i2i22-22222i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i2-12-1-2-211ii−i−i−2i−2i2i2i-12-1-1-1-1-2111112i−2i−iiii−i−i−i−iii00000000000000000000000000−i3i300i3−i30000−333−300000000
χ4622-2-2−2i−2i2i2i22-22222i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i2-12-1-2-211ii−i−i−2i−2i2i2i-12-1-1-1-1-2111112i−2i−iiii−i−i−i−iii00000000000000000000000000i3−i300−i3i300003−3−3300000000
χ4722-2-2−2i−2i2i2i22-22222i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i-12-1211-2-2−2i−2i2i2iii−i−i-1-12-1-1-11-21111−ii2i−2iii−i−i−i−iii0000000000000000000000000000000000000000ζ10−ζ26−ζ10+ζ26−ζ10+ζ26ζ10−ζ26ζ14−ζ46−ζ14+ζ46−ζ14+ζ46ζ14−ζ46
χ4822-2-2−2i−2i2i2i22-22222i−2i-2-2-2-2−2i−2i2i2i2i2i−2i−2i-12-1211-2-2−2i−2i2i2iii−i−i-1-12-1-1-11-21111−ii2i−2iii−i−i−i−iii0000000000000000000000000000000000000000−ζ10+ζ26ζ10−ζ26ζ10−ζ26−ζ10+ζ26−ζ14+ζ46ζ14−ζ46ζ14−ζ46−ζ14+ζ46
χ4922-2-2−2i−2i2i2i-222-2-22−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i2-12-1-2-211ii−i−i−2i−2i2i2i-1-2111-12-1-1-111−2i2ii−iiiii−i−i−i−i0000000000000000000000002-2-1-1−2i2i110000ii−i−i00000000
χ5022-2-2−2i−2i2i2i-222-2-22−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i2-12-1-2-211ii−i−i−2i−2i2i2i-1-2111-12-1-1-111−2i2ii−iiiii−i−i−i−i000000000000000000000000-22112i−2i-1-10000−i−iii00000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.