Finite Group Databasebeta

← Group #72260098

Character table — Group #72260098

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size112222288888888888899999918181818181818181818181818181854545454545454541122222888888888888999999181818181818181818181818181818545454545454545411222228888888888889999991818181818181818181818181818185454545454545454
order1223666333666666666224444244666612121212121212128888888836636663336666666666612121212612126666121212121212121224242424242424243663666333666666666661212121261212666612121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ61111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131111111111111111111-1-1ii−i−i-1i−i-1-1-1-1iiii−i−i−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ71111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ81111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231111111111111111111-1-1−i−iii-1−ii-1-1-1-1−i−i−i−iiiiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ911-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-11-11-11-11-111-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-11-11-11-11-111-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-11-11-11-11-1
χ1011-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-1-11-11-11-1111-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-1-11-11-11-1111-111-1-1111111-1-1-1-1-1-1111111-1-1-11-1-1111-1-111-1-1-11-11-11-11
χ1111-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111i−ii−i−ii−ii11-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111i−ii−i−ii−ii11-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111i−ii−i−ii−ii
χ1211-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111−ii−iii−ii−i11-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111−ii−iii−ii−i11-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111−ii−iii−ii−i
χ1311-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ1311-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ1311-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ1411-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ1311-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ1311-111-1-1111111-1-1-1-1-1-1-1-1ii−i−i1−ii-111-1ii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ1511-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2311-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2311-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ1611-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2311-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2311-111-1-1111111-1-1-1-1-1-1-1-1−i−iii1i−i-111-1−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ17222-1-1-1-12-1-12-1-122-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-100000000222-1-1-1-12-1-12-1-122-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-100000000222-1-1-1-12-1-12-1-122-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ18222-1-1-1-12-1-12-1-122-1-1-1-122-2-2-2-22-2-2-1-1-1-11111111100000000222-1-1-1-12-1-12-1-122-1-1-1-122-2-2-2-22-2-2-1-1-1-11111111100000000222-1-1-1-12-1-12-1-122-1-1-1-122-2-2-2-22-2-2-1-1-1-11111111100000000
χ19222-1-1-1-12-1-12-1-122-1-1-1-1-2-22i2i−2i−2i-22i−2i1111−i−i−i−iiiii00000000222-1-1-1-12-1-12-1-122-1-1-1-1-2-22i2i−2i−2i-22i−2i1111−i−i−i−iiiii00000000222-1-1-1-12-1-12-1-122-1-1-1-1-2-22i2i−2i−2i-22i−2i1111−i−i−i−iiiii00000000
χ20222-1-1-1-12-1-12-1-122-1-1-1-1-2-2−2i−2i2i2i-2−2i2i1111iiii−i−i−i−i00000000222-1-1-1-12-1-12-1-122-1-1-1-1-2-2−2i−2i2i2i-2−2i2i1111iiii−i−i−i−i00000000222-1-1-1-12-1-12-1-122-1-1-1-1-2-2−2i−2i2i2i-2−2i2i1111iiii−i−i−i−i00000000
χ2122-2-1-1112-1-12-1-1-2-21111222222-2-2-2-111-1-1-111-1-1110000000022-2-1-1112-1-12-1-1-2-21111222222-2-2-2-111-1-1-111-1-1110000000022-2-1-1112-1-12-1-1-2-21111222222-2-2-2-111-1-1-111-1-11100000000
χ2222-2-1-1112-1-12-1-1-2-2111122-2-2-2-2-222-111-111-1-111-1-10000000022-2-1-1112-1-12-1-1-2-2111122-2-2-2-2-222-111-111-1-111-1-10000000022-2-1-1112-1-12-1-1-2-2111122-2-2-2-2-222-111-111-1-111-1-100000000
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χ2422-2-1-1112-1-12-1-1-2-21111-2-2−2i−2i2i2i22i−2i1-1-11ii−i−i−i−iii0000000022-2-1-1112-1-12-1-1-2-21111-2-2−2i−2i2i2i22i−2i1-1-11ii−i−i−i−iii0000000022-2-1-1112-1-12-1-1-2-21111-2-2−2i−2i2i2i22i−2i1-1-11ii−i−i−i−iii00000000
χ252-202-200222-2-2-20000002-22i−2i2i−2i000200-22i−2i002i−2i00000000002-202-200222-2-2-20000002-22i−2i2i−2i000200-22i−2i002i−2i00000000002-202-200222-2-2-20000002-22i−2i2i−2i000200-22i−2i002i−2i0000000000
χ262-202-200222-2-2-20000002-2−2i2i−2i2i000200-2−2i2i00−2i2i00000000002-202-200222-2-2-20000002-2−2i2i−2i2i000200-2−2i2i00−2i2i00000000002-202-200222-2-2-20000002-2−2i2i−2i2i000200-2−2i2i00−2i2i0000000000
χ272-202-200222-2-2-2000000-222-2-22000-20022-200-2200000000002-202-200222-2-2-2000000-222-2-22000-20022-200-2200000000002-202-200222-2-2-2000000-222-2-22000-20022-200-220000000000
χ282-202-200222-2-2-2000000-22-222-2000-2002-22002-200000000002-202-200222-2-2-2000000-22-222-2000-2002-22002-200000000002-202-200222-2-2-2000000-22-222-2000-2002-22002-20000000000
χ292-20-11−i3i32-1-1-21100−i3−i3i3i32-22i−2i2i−2i000-1−i3i31−ii3−3−ii3−3000000002-20-11−i3i32-1-1-21100−i3−i3i3i32-22i−2i2i−2i000-1−i3i31−ii3−3−ii3−3000000002-20-11−i3i32-1-1-21100−i3−i3i3i32-22i−2i2i−2i000-1−i3i31−ii3−3−ii3−300000000
χ302-20-11−i3i32-1-1-21100−i3−i3i3i32-2−2i2i−2i2i000-1−i3i31i−i−33i−i−33000000002-20-11−i3i32-1-1-21100−i3−i3i3i32-2−2i2i−2i2i000-1−i3i31i−i−33i−i−33000000002-20-11−i3i32-1-1-21100−i3−i3i3i32-2−2i2i−2i2i000-1−i3i31i−i−33i−i−3300000000
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χ4088-888-8-8-1-1-1-1-1-11111110000000000000000000000000000088-888-8-8-1-1-1-1-1-11111110000000000000000000000000000088-888-8-8-1-1-1-1-1-111111100000000000000000000000000000
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χ438-808-800-1-1-11113-33-3-33000000000000000000000000000008-808-800-1-1-11113-33-3-33000000000000000000000000000008-808-800-1-1-11113-33-3-3300000000000000000000000000000
χ448-808-800-1-1-1111-33-333-3000000000000000000000000000008-808-800-1-1-1111-33-333-3000000000000000000000000000008-808-800-1-1-1111-33-333-300000000000000000000000000000
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χ10711-111-1-1111111-1-1-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-111i−ii−i−ii−ii−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32ζ22−ζ22ζ22−ζ22−ζ22ζ22−ζ22ζ22−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32ζ14−ζ14ζ14−ζ14−ζ14ζ14−ζ14ζ14
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χ1398-808-800-1-1-11113-33-3-3300000000000000000000000000000−4−4i34+4i30−4−4i34+4i3001+i321+i321+i32−1−i32−1−i32−1−i32−3−3i323+3i32−3−3i323+3i323+3i32−3−3i3200000000000000000000000000000−4+4i34−4i30−4+4i34−4i3001−i321−i321−i32−1+i32−1+i32−1+i32−3+3i323−3i32−3+3i323−3i323−3i32−3+3i3200000000000000000000000000000
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χ1418-80-44−4i34i3-11−3i321+3i321−1+3i32−1−3i323-3−3+i323+i323−i32−3−i3200000000000000000000000000000−4−4i34+4i302+2i3−2−2i3−6+2i36−2i31+i32−5+i322−i3−1−i325−i32−2+i3−3−3i323+3i323+i32−i3−3−i32i300000000000000000000000000000−4+4i34−4i302−2i3−2+2i36+2i3−6−2i31−i322+i3−5−i32−1+i32−2−i35+i32−3+3i323−3i32−i3−3+i32i33−i3200000000000000000000000000000
χ1428-80-44−4i34i3-11+3i321−3i321−1−3i32−1+3i32-333+i32−3+i32−3−i323−i3200000000000000000000000000000−4−4i34+4i302+2i3−2−2i3−6+2i36−2i31+i322−i3−5+i32−1−i32−2+i35−i323+3i32−3−3i32−i33+i32i3−3−i3200000000000000000000000000000−4+4i34−4i302−2i3−2+2i36+2i3−6−2i31−i32−5−i322+i3−1+i325+i32−2−i33−3i32−3+3i32−3+i32−i33−i32i300000000000000000000000000000
χ1438-80-444i3−4i3-11−3i321+3i321−1+3i32−1−3i32-333−i32−3−i32−3+i323+i3200000000000000000000000000000−4−4i34+4i302+2i3−2−2i36−2i3−6+2i31+i32−5+i322−i3−1−i325−i32−2+i33+3i32−3−3i32−3−i32i33+i32−i300000000000000000000000000000−4+4i34−4i302−2i3−2+2i3−6−2i36+2i31−i322+i3−5−i32−1+i32−2−i35+i323−3i32−3+3i32i33−i32−i3−3+i3200000000000000000000000000000
χ1448-80-444i3−4i3-11+3i321−3i321−1−3i32−1+3i323-3−3−i323−i323+i32−3+i3200000000000000000000000000000−4−4i34+4i302+2i3−2−2i36−2i3−6+2i31+i322−i3−5+i32−1−i32−2+i35−i32−3−3i323+3i32i3−3−i32−i33+i3200000000000000000000000000000−4+4i34−4i302−2i3−2+2i3−6−2i36+2i31−i32−5−i322+i3−1+i325+i32−2−i3−3+3i323−3i323−i32i3−3+i32−i300000000000000000000000000000

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