Finite Group Databasebeta

← Group #13157218

Character table — Group #13157218

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size111122222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441818181836363636363636363636108108108108108108108108
order122222366666663333334466666666666666666666666666666666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212444444121212121212121288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ511111111111111111111-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1
χ611111111111111111111-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111
χ711111111111111111111-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii
χ811111111111111111111-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i
χ91-11-11-1111-1-1-11-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13
χ101-11-11-1111-1-1-11-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13
χ111-11-11-1111-1-1-11-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23
χ121-11-11-1111-1-1-11-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iiiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23
χ131-11-11-1111-1-1-11-1111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111ii−i−i−iiii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ141-11-11-1111-1-1-11-1111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111ii−i−i−iiii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ151-11-11-1111-1-1-11-1111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111−i−iiii−i−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ161-11-11-1111-1-1-11-1111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111−i−iiii−i−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ17222222-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ18222222-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ19222222-1-1-1-1-1-1-1-122-1-1-1-1-2-22222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-11111-2-2-2-2-2-2-2-21111111111111111-2-2-2-2-2-2-2-211111111111111112222-2-2-1-1-1-1111100000000
χ20222222-1-1-1-1-1-1-1-122-1-1-1-1-2-22222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-11111-2-2-2-2-2-2-2-21111111111111111-2-2-2-2-2-2-2-21111111111111111-2-2-2-2221111-1-1-1-100000000
χ212222-2-22-2-22-2-22222222200-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-222222200000000000000000000000000000000000000000000000000002-22-2002-22-2000000000000
χ222222-2-22-2-22-2-22222222200-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000-22-2200-22-22000000000000
χ232222-2-2-111-111-1-122-1-1-1-100-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111122-1-1-1-1−i3i3−i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-22-200-11-11−i3i3−i3i300000000
χ242222-2-2-111-111-1-122-1-1-1-100-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111122-1-1-1-1−i3i3−i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-22-22001-11-1i3−i3i3−i300000000
χ252222-2-2-111-111-1-122-1-1-1-100-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111122-1-1-1-1i3−i3i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-22-200-11-11i3−i3i3−i300000000
χ262222-2-2-111-111-1-122-1-1-1-100-2-2-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111122-1-1-1-1i3−i3i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-22-22001-11-1−i3i3−i3i300000000
χ272-22-22-2-1-1-1111-1122-1-1-1-12-22222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111122-1-1-1-1-1-11122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111112i2i−2i−2i2i−2i−i−iii−i−iii00000000
χ282-22-22-2-1-1-1111-1122-1-1-1-12-22222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111122-1-1-1-1-1-11122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111−2i−2i2i2i−2i2iii−i−iii−i−i00000000
χ292-22-22-2-1-1-1111-1122-1-1-1-1-222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111122-1-1-1-111-1-1-2-2-2-2-2-2-2-2111111111111111122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12i2i−2i−2i−2i2i−i−iiiii−i−i00000000
χ302-22-22-2-1-1-1111-1122-1-1-1-1-222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111122-1-1-1-111-1-1-2-2-2-2-2-2-2-2111111111111111122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−2i−2i2i2i2i−2iii−i−i−i−iii00000000
χ312-22-2-222-2-2-2222-222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222222222200000000000000000000000000000000000000000000000000002i−2i−2i2i002i−2i−2i2i000000000000
χ322-22-2-222-2-2-2222-222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222222222220000000000000000000000000000000000000000000000000000−2i2i2i−2i00−2i2i2i−2i000000000000
χ332-22-2-22-1111-1-1-1122-1-1-1-100-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-122-1-1-1-1−i3i3i3−i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32i−2i−2i2i00−iii−i3−3−3300000000
χ342-22-2-22-1111-1-1-1122-1-1-1-100-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-122-1-1-1-1−i3i3i3−i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3−2i2i2i−2i00i−i−ii−333−300000000
χ352-22-2-22-1111-1-1-1122-1-1-1-100-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-122-1-1-1-1i3−i3−i3i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32i−2i−2i2i00−iii−i−333−300000000
χ362-22-2-22-1111-1-1-1122-1-1-1-100-2-2-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-122-1-1-1-1i3−i3−i3i300000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300000000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−2i2i2i−2i00i−i−ii3−3−3300000000
χ37444444444444441-211-2-24411-2-21111-2-2-2-211-2-211-2-21111-2-2-2-21111-2-2-2-21-211-2-244441111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-20000000000000000000000
χ38444444444444441-211-2-2-4-411-2-21111-2-2-2-211-2-211-2-21111-2-2-2-21111-2-2-2-21-211-2-2-4-4-4-4-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-122220000000000000000000000
χ3944444444444444-21-2-21144-2-211-2-2-2-21111-2-211-2-211-2-2-2-21111-2-2-2-21111-21-2-2114444-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-21111-2-2-2-211110000000000000000000000
χ4044444444444444-21-2-211-4-4-2-211-2-2-2-21111-2-211-2-211-2-2-2-21111-2-2-2-21111-21-2-211-4-4-4-42222-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-12222-1-1-1-10000000000000000000000
χ41444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i32114411-2-2−1−3i32−1−3i32−1+3i32−1+3i32111111-2-211-2-2−1−3i32−1−3i32−1+3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-2-2-2-21111-2-2-2-2−1−3i32−1−3i32−1+3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i3211111111-2-2-2-2−1−3i32−1−3i32−1+3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i3211110000000000000000000000
χ42444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i3211-4-411-2-2−1−3i32−1−3i32−1+3i32−1+3i32111111-2-211-2-2−1−3i32−1−3i32−1+3i32−1+3i321111−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i32112222-1-1-1-122221+3i321+3i321−3i321−3i32-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-1-1-1-1-122221+3i321+3i321−3i321−3i32-1-1-1-11+3i321+3i321−3i321−3i32-1-1-1-10000000000000000000000
χ43444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i32114411-2-2−1+3i32−1+3i32−1−3i32−1−3i32111111-2-211-2-2−1+3i32−1+3i32−1−3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-2-2-2-21111-2-2-2-2−1+3i32−1+3i32−1−3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i3211111111-2-2-2-2−1+3i32−1+3i32−1−3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i3211110000000000000000000000
χ44444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i3211-4-411-2-2−1+3i32−1+3i32−1−3i32−1−3i32111111-2-211-2-2−1+3i32−1+3i32−1−3i32−1−3i321111−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i32112222-1-1-1-122221−3i321−3i321+3i321+3i32-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-1-1-1-1-122221−3i321−3i321+3i321+3i32-1-1-1-11−3i321−3i321+3i321+3i32-1-1-1-10000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.