Finite Group Databasebeta

← Group #13139965

Character table — Group #13139965

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152
size111111112222222266666666666666661212121212121212181818181818181818181818181818181818181818181818181818181818181818181818111111112222222266666666666666661212121212121212181818181818181818181818181818181818181818181818181818181818181818181818
order1222444436661212121233666666121212121212121236661212121244448888888812121212121212122424242424242424242424242424242422224444666612121212666666661212121212121212666612121212444488888888121212121212121224242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i1-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i1-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ101-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i1-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i1-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ111-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i-11−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-111−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i-11−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-111−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ121-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i-11−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-111−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-11-1i−ii−i11-1-1i−ii−i111-1-1-11-1iii−i−i−ii−i11-1-1ii−i−i-11−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-111−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ131-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii1-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii1-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ141-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii1-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii1-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ151-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii-11i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-111ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii-11i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-111ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ161-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii-11i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-111ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-11-1−ii−ii11-1-1−ii−ii111-1-1-11-1−i−i−iiii−ii11-1-1−i−iii-11i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-111ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ1722222222222222222-1222-1-1-12-1-12-1-122-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-1000000000000000022222222222222222-1222-1-1-12-1-12-1-122-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222-1222-1-1-12-1-12-1-122-1-1-1-1-1-1-1-1-2-2-2-20000000011111111000000000000000022222222222222222-1222-1-1-12-1-12-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000111111110000000000000000
χ192222222222222222-12-1-1-1222-122-122-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-12222222222222222-12-1-1-1222-122-122-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222-12-1-1-1222-122-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000000000000000111111112222222222222222-12-1-1-1222-122-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ212222-2-2-2-22222-2-2-2-22-1222-1-1-1-211-211-2-2-1-1-1-1111122-2-200000000-1-1-1-1111100000000000000002222-2-2-2-22222-2-2-2-22-1222-1-1-1-211-211-2-2-1-1-1-1111122-2-200000000-1-1-1-111110000000000000000
χ222222-2-2-2-22222-2-2-2-22-1222-1-1-1-211-211-2-2-1-1-1-11111-2-222000000001111-1-1-1-100000000000000002222-2-2-2-22222-2-2-2-22-1222-1-1-1-211-211-2-2-1-1-1-11111-2-222000000001111-1-1-1-10000000000000000
χ232222-2-2-2-22222-2-2-2-2-12-1-1-12221-2-21-2-211-1-1-1-11111000000002i2i−2i−2i0000000000000000−i−i−i−iiiii2222-2-2-2-22222-2-2-2-2-12-1-1-12221-2-21-2-211-1-1-1-11111000000002i2i−2i−2i0000000000000000−i−i−i−iiiii
χ242222-2-2-2-22222-2-2-2-2-12-1-1-12221-2-21-2-211-1-1-1-1111100000000−2i−2i2i2i0000000000000000iiii−i−i−i−i2222-2-2-2-22222-2-2-2-2-12-1-1-12221-2-21-2-211-1-1-1-1111100000000−2i−2i2i2i0000000000000000iiii−i−i−i−i
χ2522-2-222-2-22-2-2222-2-222-2-222-2-222-222-2-2-22-2-222-22-200000000000000000000000000000000000022-2-222-2-22-2-2222-2-222-2-222-2-222-222-2-2-22-2-222-22-2000000000000000000000000000000000000
χ2622-2-222-2-22-2-2222-2-22-1-2-22-1112-112-11-2-2-111-1-11-110000000000003−33−33−33−3000000000000000022-2-222-2-22-2-2222-2-22-1-2-22-1112-112-11-2-2-111-1-11-110000000000003−33−33−33−30000000000000000
χ2722-2-222-2-22-2-2222-2-22-1-2-22-1112-112-11-2-2-111-1-11-11000000000000−33−33−33−33000000000000000022-2-222-2-22-2-2222-2-22-1-2-22-1112-112-11-2-2-111-1-11-11000000000000−33−33−33−330000000000000000
χ2822-2-222-2-22-2-2222-2-2-1211-12-2-2-12-2-12-211-111-1-11-1100000000000000000000000000003−33−33−33−322-2-222-2-22-2-2222-2-2-1211-12-2-2-12-2-12-211-111-1-11-1100000000000000000000000000003−33−33−33−3
χ2922-2-222-2-22-2-2222-2-2-1211-12-2-2-12-2-12-211-111-1-11-110000000000000000000000000000−33−33−33−3322-2-222-2-22-2-2222-2-2-1211-12-2-2-12-2-12-211-111-1-11-110000000000000000000000000000−33−33−33−33
χ3022-2-2-2-2222-2-22-2-22222-2-222-2-2-2-22-2-22222-2-22-22-2200000000000000000000000000000000000022-2-2-2-2222-2-22-2-22222-2-222-2-2-2-22-2-22222-2-22-22-22000000000000000000000000000000000000
χ3122-2-2-2-2222-2-22-2-2222-1-2-22-111-21-1-21-122-111-11-11-10000000000003−33−3−33−33000000000000000022-2-2-2-2222-2-22-2-2222-1-2-22-111-21-1-21-122-111-11-11-10000000000003−33−3−33−330000000000000000
χ3222-2-2-2-2222-2-22-2-2222-1-2-22-111-21-1-21-122-111-11-11-1000000000000−33−333−33−3000000000000000022-2-2-2-2222-2-22-2-2222-1-2-22-111-21-1-21-122-111-11-11-1000000000000−33−333−33−30000000000000000
χ3322-2-2-2-2222-2-22-2-222-1211-12-2-21-221-22-1-1-111-11-11-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i322-2-2-2-2222-2-22-2-222-1211-12-2-21-221-22-1-1-111-11-11-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ3422-2-2-2-2222-2-22-2-222-1211-12-2-21-221-22-1-1-111-11-11-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i322-2-2-2-2222-2-22-2-222-1211-12-2-21-221-22-1-1-111-11-11-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ352-22-22i−2i2i−2i22-2-22i−2i2i−2i2-12-2-21-112i−i−i−2iii2i−2i-1-111−i−iii2-22i−2i00000000-1-111−i−iii00000000000000002-22-22i−2i2i−2i22-2-22i−2i2i−2i2-12-2-21-112i−i−i−2iii2i−2i-1-111−i−iii2-22i−2i00000000-1-111−i−iii0000000000000000
χ362-22-22i−2i2i−2i22-2-22i−2i2i−2i2-12-2-21-112i−i−i−2iii2i−2i-1-111−i−iii-22−2i2i0000000011-1-1ii−i−i00000000000000002-22-22i−2i2i−2i22-2-22i−2i2i−2i2-12-2-21-112i−i−i−2iii2i−2i-1-111−i−iii-22−2i2i0000000011-1-1ii−i−i0000000000000000
χ372-22-22i−2i2i−2i22-2-22i−2i2i−2i-12-111-22-2−i2i2ii−2i−2i−ii-1-111−i−iii000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ132-22-22i−2i2i−2i22-2-22i−2i2i−2i-12-111-22-2−i2i2ii−2i−2i−ii-1-111−i−iii000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ382-22-22i−2i2i−2i22-2-22i−2i2i−2i-12-111-22-2−i2i2ii−2i−2i−ii-1-111−i−iii00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ132-22-22i−2i2i−2i22-2-22i−2i2i−2i-12-111-22-2−i2i2ii−2i−2i−ii-1-111−i−iii00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.