Finite Group Databasebeta

← Group #13135942

Character table — Group #13135942

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146
size11111111111122222222222222222244444444444466666666666666666666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636
order123344661212121224668888121224242424242424242466881212242424243333666666666666121212121212121212121212121212126666666612121212121212122424242424242424242424242424242424242424242424242424242424242424161616161616161648484848484848484848484848484848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-111-1-1-1-11-111ii−i−i-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ101111-1-111-1-1-1-11-111ii−i−i-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ111111-1-111-1-1-1-11-111ii−i−i-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ121111-1-111-1-1-1-11-111ii−i−i-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ131111-1-111-1-1-1-11-111−i−iii-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ141111-1-111-1-1-1-11-111−i−iii-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ151111-1-111-1-1-1-11-111−i−iii-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ161111-1-111-1-1-1-11-111−i−iii-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ172222222222222222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000
χ18222222222222222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000
χ19222222222222222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000
χ20222222222222222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000
χ21222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000000000000000
χ22222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000000000000000
χ23222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-211-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-211000000000000000000000000
χ24222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2000000000000000000000000
χ252222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111-2-2111111-2-2111111000000000000000000000000
χ262222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-2111111-2-2111111-2-21111000000000000000000000000
χ272222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-2111111-2-2111111-2-211000000000000000000000000
χ282222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2111111-2-2111111-2-2000000000000000000000000
χ292222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-222222-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111-2-2111111-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000
χ302222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-12-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-2111111-2-2111111-2-21111-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000
χ312222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-1-12-1-1-1-1-122-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-2111111-2-2111111-2-211-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000000000
χ322222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2111111-2-2111111-2-2-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000000000
χ33222222222222-2-2-2-22-22-2-2-222-2-222-2-20000000000002222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000002-22-22-22-22-22-22-22-20000000000000000000000000000000000000000
χ34222222222222-2-2-2-22-22-2-2-222-2-222-2-20000000000002-1-1-1-2-21111112-1-1-1-2-211111122-1-1-1-1-1-100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i32-2-11-11-112-2-11-11-1100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000000
χ35222222222222-2-2-2-22-22-2-2-222-2-222-2-20000000000002-1-1-1-2-21111112-1-1-1-2-211111122-1-1-1-1-1-100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i32-2-11-11-112-2-11-11-1100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000000
χ36222222222222-2-2-2-22-22-2-2-222-2-222-2-2000000000000-12-1-111-2-21111-12-1-111-2-21111-1-122-1-1-1-1−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3-112-2-11-11-112-2-11-11−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000000000
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χ38222222222222-2-2-2-22-22-2-2-222-2-222-2-2000000000000-1-12-11111-2-211-1-12-11111-2-211-1-1-1-122-1-1−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3-11-112-2-11-11-112-2-11−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000000000
χ39222222222222-2-2-2-22-22-2-2-222-2-222-2-2000000000000-1-12-11111-2-211-1-12-11111-2-211-1-1-1-122-1-1i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3-11-112-2-11-11-112-2-11i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000000000000
χ40222222222222-2-2-2-22-22-2-2-222-2-222-2-2000000000000-1-1-12111111-2-2-1-1-12111111-2-2-1-1-1-1-1-122−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300-11-11-112-2-11-11-112-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000000000000
χ41222222222222-2-2-2-22-22-2-2-222-2-222-2-2000000000000-1-1-12111111-2-2-1-1-12111111-2-2-1-1-1-1-1-122i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300-11-11-112-2-11-11-112-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000000000000
χ42222222222222-2-2-2-2-22-22-2-2-2-222-2-2220000000000002222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000-22-22-22-22-22-22-22-220000000000000000000000000000000000000000
χ43222222222222-2-2-2-2-22-22-2-2-2-222-2-2220000000000002-1-1-1-2-21111112-1-1-1-2-211111122-1-1-1-1-1-100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3-221-11-11-1-221-11-11-100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000000000
χ44222222222222-2-2-2-2-22-22-2-2-2-222-2-2220000000000002-1-1-1-2-21111112-1-1-1-2-211111122-1-1-1-1-1-100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3-221-11-11-1-221-11-11-100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000000000
χ45222222222222-2-2-2-2-22-22-2-2-2-222-2-222000000000000-12-1-111-2-21111-12-1-111-2-21111-1-122-1-1-1-1−i3i300−i3i3i3−i3−i3i300−i3i3i3−i31-1-221-11-11-1-221-11-1i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000000000
χ46222222222222-2-2-2-2-22-22-2-2-2-222-2-222000000000000-12-1-111-2-21111-12-1-111-2-21111-1-122-1-1-1-1i3−i300i3−i3−i3i3i3−i300i3−i3−i3i31-1-221-11-11-1-221-11-1−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000000000
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χ14066−3+3i3−3−3i366−3+3i3−3−3i3−3+3i3−3+3i3−3−3i3−3−3i3-6-63−3i33+3i3-66-663−3i33+3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14166−3+3i3−3−3i3-6-6−3+3i3−3−3i33−3i33−3i33+3i33+3i3-663−3i33+3i36i−6i−6i6i−3+3i3−3−3i36ζ146ζ22−6ζ14−6ζ22−6ζ14−6ζ226ζ146ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14266−3+3i3−3−3i3-6-6−3+3i3−3−3i33−3i33−3i33+3i33+3i3-663−3i33+3i3−6i6i6i−6i−3+3i3−3−3i3−6ζ14−6ζ226ζ146ζ226ζ146ζ22−6ζ14−6ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14312-12−6−6i3−6+6i312i−12i6+6i36−6i312ζ22−12ζ2212ζ14−12ζ1400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14412-12−6−6i3−6+6i3−12i12i6+6i36−6i3−12ζ2212ζ22−12ζ1412ζ1400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14512-12−6+6i3−6−6i312i−12i6−6i36+6i312ζ14−12ζ1412ζ22−12ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ14612-12−6+6i3−6−6i3−12i12i6−6i36+6i3−12ζ1412ζ14−12ζ2212ζ2200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.