Finite Group Databasebeta

← Group #11857367

Character table — Group #11857367

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size1111111122222222222222224444444444444444444444444466666666121212121212121212121212121212121212121218181818363611111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order12224444336666661212121212121212366688121212122424242424242424242424242424242422224444666688881212121224242424242424242244882222444466666666121212121212121266668812121212242424242424242424242424242424242222444466668888121212122424242424242424224488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111111111111111111111111111111111111111111111-1-111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1
χ91111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i11-1-1i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i11-1-1i−i
χ101111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111-1-1i−i−ii-1-111ii−i−i−i−iii-1-111−ii1111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111-1-1i−i−ii-1-111ii−i−i−i−iii-1-111−ii
χ111111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-111−iii−i11-1-1−i−iiiii−i−i-1-111−ii1111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-111−iii−i11-1-1−i−iiiii−i−i-1-111−ii
χ121111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1−ii−ii1111−i−iii−i−iii11-1-1i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1−ii−ii1111−i−iii−i−iii11-1-1i−i
χ131111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111−ii−ii-1-1-1-1−i−iii−i−iii11-1-1−ii1111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111−ii−ii-1-1-1-1−i−iii−i−iii11-1-1−ii
χ141111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111-1-1−iii−i-1-111−i−iiiii−i−i-1-111i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111-1-1−iii−i-1-111−i−iiiii−i−i-1-111i−i
χ151111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-111i−i−ii11-1-1ii−i−i−i−iii-1-111i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-111i−i−ii11-1-1ii−i−i−i−iii-1-111i−i
χ161111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1i−ii−i1111ii−i−iii−i−i11-1-1−ii1111-1-1-1-111111111-1-1-1-1-1-1-1-11111−ii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1i−ii−i1111ii−i−iii−i−i11-1-1−ii
χ17222222222-122-1-12-122-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10022002200-1-1002200-1-10000-1-1-1-1000000222222222-122-1-12-122-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10022002200-1-1002200-1-10000-1-1-1-1000000
χ18222222222-122-1-12-122-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100-2-200-2-2001100-2-2001100001111000000222222222-122-1-12-122-1-122-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100-2-200-2-2001100-2-2001100001111000000
χ19222222222-122-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-2-211-2-211111111110022002200-1-100-2-200-1-100001111000000222222222-122-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-2-211-2-211111111110022002200-1-100-2-200-1-100001111000000
χ20222222222-122-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-2-211-2-2111111111100-2-200-2-20011002200110000-1-1-1-1000000222222222-122-1-12-122-1-122-1-1-1-1-1-1-2-2-1-1-1-1-2-211-2-2111111111100-2-200-2-20011002200110000-1-1-1-1000000
χ2122222222-12-1-122-12-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122002200-1-1002200-1-100-1-1-1-1000000000022222222-12-1-122-12-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122002200-1-1002200-1-100-1-1-1-10000000000
χ2222222222-12-1-122-12-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-200-2-2001100-2-20011001111000000000022222222-12-1-122-12-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-200-2-2001100-2-200110011110000000000
χ2322222222-12-1-122-12-1-122-1-122-1-1-1-1-2-2-1-1-1-111-2-211-2-21111111122002200-1-100-2-200-1-1001111000000000022222222-12-1-122-12-1-122-1-122-1-1-1-1-2-2-1-1-1-111-2-211-2-21111111122002200-1-100-2-200-1-10011110000000000
χ2422222222-12-1-122-12-1-122-1-122-1-1-1-1-2-2-1-1-1-111-2-211-2-211111111-2-200-2-200110022001100-1-1-1-1000000000022222222-12-1-122-12-1-122-1-122-1-1-1-1-2-2-1-1-1-111-2-211-2-211111111-2-200-2-200110022001100-1-1-1-10000000000
χ252222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-12i−2i11112i2i−i−i−2i−2iii−i−i−i−iiiii002200-2-200-1-1002i−2i00110000−i−iii0000002222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-12i−2i11112i2i−i−i−2i−2iii−i−i−i−iiiii002200-2-200-1-1002i−2i00110000−i−iii000000
χ262222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-12i−2i11112i2i−i−i−2i−2iii−i−i−i−iiiii00-2-20022001100−2i2i00-1-10000ii−i−i0000002222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-12i−2i11112i2i−i−i−2i−2iii−i−i−i−iiiii00-2-20022001100−2i2i00-1-10000ii−i−i000000
χ272222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-1−2i2i1111−2i−2iii2i2i−i−iiiii−i−i−i−i002200-2-200-1-100−2i2i00110000ii−i−i0000002222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-1−2i2i1111−2i−2iii2i2i−i−iiiii−i−i−i−i002200-2-200-1-100−2i2i00110000ii−i−i000000
χ282222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-1−2i2i1111−2i−2iii2i2i−i−iiiii−i−i−i−i00-2-200220011002i−2i00-1-10000−i−iii0000002222-2-2-2-22-122-1-12-1-2-211-2-211-1-1-1-1−2i2i1111−2i−2iii2i2i−i−iiiii−i−i−i−i00-2-200220011002i−2i00-1-10000−i−iii000000
χ292222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-12i−2i1111−i−i2i2iii−2i−2i−i−i−i−iiiii2200-2-200-1-1002i−2i001100−i−iii00000000002222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-12i−2i1111−i−i2i2iii−2i−2i−i−i−i−iiiii2200-2-200-1-1002i−2i001100−i−iii0000000000
χ302222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-12i−2i1111−i−i2i2iii−2i−2i−i−i−i−iiiii-2-20022001100−2i2i00-1-100ii−i−i00000000002222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-12i−2i1111−i−i2i2iii−2i−2i−i−i−i−iiiii-2-20022001100−2i2i00-1-100ii−i−i0000000000
χ312222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-1−2i2i1111ii−2i−2i−i−i2i2iiiii−i−i−i−i2200-2-200-1-100−2i2i001100ii−i−i00000000002222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-1−2i2i1111ii−2i−2i−i−i2i2iiiii−i−i−i−i2200-2-200-1-100−2i2i001100ii−i−i0000000000
χ322222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-1−2i2i1111ii−2i−2i−i−i2i2iiiii−i−i−i−i-2-200220011002i−2i00-1-100−i−iii00000000002222-2-2-2-2-12-1-122-1211-2-211-2-2-1-1-1-1−2i2i1111ii−2i−2i−i−i2i2iiiii−i−i−i−i-2-200220011002i−2i00-1-100−i−iii0000000000
χ3322-2-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i0000000000000000002-2002i−2i002-20000002i−2i0000000000000022-2-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i0000000000000000002-2002i−2i002-20000002i−2i00000000000000
χ3422-2-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i000000000000000000-2200−2i2i00-22000000−2i2i0000000000000022-2-22i−2i2i−2i222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-2002i−2i2i−2i000000000000000000-2200−2i2i00-22000000−2i2i00000000000000
χ3522-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13002-2002i−2i00-11000000−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000022-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13002-2002i−2i00-11000000−ii0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ3622-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300-2200−2i2i001-1000000i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000022-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300-2200−2i2i001-1000000i−i0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ3722-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13002-2002i−2i00-11000000−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000022-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13002-2002i−2i00-11000000−ii0000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ3822-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300-2200−2i2i001-1000000i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000022-2-22i−2i2i−2i2-12-2-11-212i−2i−ii2i−2i−ii-1-11100−ii−ii00ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ1300-2200−2i2i001-1000000i−i0000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ3922-2-2−2i2i−2i2i222-22-2-2-2−2i2i−2i2i−2i2i−2i2i22-2-200−2i2i−2i2i0000000000000000002-200−2i2i002-2000000−2i2i0000000000000022-2-2−2i2i−2i2i222-22-2-2-2−2i2i−2i2i−2i2i−2i2i22-2-200−2i2i−2i2i0000000000000000002-200−2i2i002-2000000−2i2i00000000000000
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χ1604-44-4−4i4i4i−4i-2-22-22-222−2i2i−2i2i2i−2i2i−2i1-11-100−iii−i2ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000000000000000000000-44-444i−4i−4i4i22-22-22-2-22i−2i2i−2i−2i2i−2i2i-11-1100i−i−ii−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000000000000000000000
χ1614-4-4444-4-44-2-4-4224-2-4-42244-2-2-222-200-2-22200000000000000000000000000000000000000000000000000-444-4-4-444-4244-2-2-4244-2-2-4-4222-2-220022-2-200000000000000000000000000000000000000000000000000
χ1624-4-4444-4-4-2422-4-4-2422-4-4-2-244-222-200-2-22200000000000000000000000000000000000000000000000000-444-4-4-4442-4-2-2442-4-2-24422-4-42-2-220022-2-200000000000000000000000000000000000000000000000000
χ1634-4-4444-4-4-2-22222-2-22222-2-2-2-21-1-110011-1-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000000000-444-4-4-44422-2-2-2-222-2-2-2-22222-111-100-1-11100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000000000
χ1644-4-4444-4-4-2-22222-2-22222-2-2-2-21-1-110011-1-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000000000-444-4-4-44422-2-2-2-222-2-2-2-22222-111-100-1-111000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000000000
χ1654-4-44-4-4444-2-4-4224-244-2-2-4-422-222-20022-2-200000000000000000000000000000000000000000000000000-444-444-4-4-4244-2-2-42-4-42244-2-22-2-2200-2-22200000000000000000000000000000000000000000000000000
χ1664-4-44-4-444-2422-4-4-24-2-24422-4-4-222-20022-2-200000000000000000000000000000000000000000000000000-444-444-4-42-4-2-2442-422-4-4-2-2442-2-2200-2-22200000000000000000000000000000000000000000000000000
χ1674-4-44-4-444-2-22222-2-2-2-2-2-222221-1-1100-1-111000000003-3-333-3-330000000000000000000000000000000000-444-444-4-422-2-2-2-2222222-2-2-2-2-111-10011-1-100000000-333-3-333-30000000000000000000000000000000000
χ1684-4-44-4-444-2-22222-2-2-2-2-2-222221-1-1100-1-11100000000-333-3-333-30000000000000000000000000000000000-444-444-4-422-2-2-2-2222222-2-2-2-2-111-10011-1-1000000003-3-333-3-330000000000000000000000000000000000

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