Finite Group Databasebeta

← Group #13181166

Character table — Group #13181166

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222224444888888888899181818181818181818181818181818181836363636727272721122222444488888888889918181818181818181818181818181818183636363672727272
order1223666336633666666664448888121212122424242424242424224466121222266666666666666666644488881212121224242424242424242244661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-1
χ4111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-11
χ511-11-1-11111111-1-111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-111-11-1-11111111-1-111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-1
χ611-11-1-11111111-1-111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-11111-11-1-11111111-1-111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-111
χ711-11-1-11111111-1-111-1-1-1-1-1-11-1-111-1-111-1-1-1-111111-1-111-1-1111-11-1-11111111-1-111-1-1-1-1-1-11-1-111-1-111-1-1-1-111111-1-111-1-11
χ811-11-1-11111111-1-111-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-111-1-111-111-11-1-11111111-1-111-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-111-1-111-1
χ9222222222222222222222-2-2-20000-2-2-2-20000000000000000222222222222222222222-2-2-20000-2-2-2-20000000000000000
χ10222-1-1-1-12222-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-100000000222-1-1-1-12222-1-122-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-100000000
χ11222-1-1-1-12222-1-122-1-1-1-1-1-1222-2-2-2-2-1-1-1-11111111100000000222-1-1-1-12222-1-122-1-1-1-1-1-1222-2-2-2-2-1-1-1-11111111100000000
χ12222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-20000111133−3−333−3−300000000222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-20000111133−3−333−3−300000000
χ13222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-200001111−3−333−3−33300000000222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-200001111−3−333−3−33300000000
χ1422-22-2-22222222-2-222-2-2-2-222-2000022-2-2000000000000000022-22-2-22222222-2-222-2-2-2-222-2000022-2-20000000000000000
χ1522-2-111-12222-1-1-2-2-1-1111122-20000-1-11133−3−3−3−3330000000022-2-111-12222-1-1-2-2-1-1111122-20000-1-11133−3−3−3−33300000000
χ1622-2-111-12222-1-1-2-2-1-1111122-20000-1-111−3−33333−3−30000000022-2-111-12222-1-1-2-2-1-1111122-20000-1-111−3−33333−3−300000000
χ1722-2-111-12222-1-1-2-2-1-11111-2-2222-2-211-1-1-1-1-1-111110000000022-2-111-12222-1-1-2-2-1-11111-2-2222-2-211-1-1-1-1-1-1111100000000
χ1822-2-111-12222-1-1-2-2-1-11111-2-22-2-22211-1-11111-1-1-1-10000000022-2-111-12222-1-1-2-2-1-11111-2-22-2-22211-1-11111-1-1-1-100000000
χ192-20200-222-2-22200-2-200002i−2i02−2−i2i22i−2i002−22−2−i2i2−i2i2000000002-20200-222-2-22200-2-200002i−2i02−2−i2i22i−2i002−22−2−i2i2−i2i200000000
χ202-20200-222-2-22200-2-200002i−2i0−22i2−i22i−2i00−22−22i2−i2i2−i2000000002-20200-222-2-22200-2-200002i−2i0−22i2−i22i−2i00−22−22i2−i2i2−i200000000
χ212-20200-222-2-22200-2-20000−2i2i02−2i2−i2−2i2i002−22−2i2−i2i2−i2000000002-20200-222-2-22200-2-20000−2i2i02−2i2−i2−2i2i002−22−2i2−i2i2−i200000000
χ222-20200-222-2-22200-2-20000−2i2i0−22−i2i2−2i2i00−22−22−i2i2−i2i2000000002-20200-222-2-22200-2-20000−2i2i0−22−i2i2−2i2i00−22−22−i2i2−i2i200000000
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χ252-20-1−i3i3122-2-2-1-10011−i3−i3i3i3−2i2i02−2i2−i2i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000002-20-1−i3i3122-2-2-1-10011−i3−i3i3i3−2i2i02−2i2−i2i−i−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ262-20-1−i3i3122-2-2-1-10011−i3−i3i3i3−2i2i0−22−i2i2i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000002-20-1−i3i3122-2-2-1-10011−i3−i3i3i3−2i2i0−22−i2i2i−i−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ272-20-1i3−i3122-2-2-1-10011i3i3−i3−i32i−2i02−2−i2i2−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000002-20-1i3−i3122-2-2-1-10011i3i3−i3−i32i−2i02−2−i2i2−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
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χ292-20-1i3−i3122-2-2-1-10011i3i3−i3−i3−2i2i02−2i2−i2i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000002-20-1i3−i3122-2-2-1-10011i3i3−i3−i3−2i2i02−2i2−i2i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ302-20-1i3−i3122-2-2-1-10011i3i3−i3−i3−2i2i0−22−i2i2i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000002-20-1i3−i3122-2-2-1-10011i3i3−i3−i3−2i2i0−22−i2i2i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ3144444441-21-21-21-21-21-21-2000000000000000000002020-10-144444441-21-21-21-21-21-21-2000000000000000000002020-10-1
χ3244444441-21-21-21-21-21-21-200000000000000000000-20-2010144444441-21-21-21-21-21-21-200000000000000000000-20-20101
χ334444444-21-21-21-21-21-21-2100000000000000000002020-10-104444444-21-21-21-21-21-21-2100000000000000000002020-10-10
χ344444444-21-21-21-21-21-21-210000000000000000000-20-2010104444444-21-21-21-21-21-21-210000000000000000000-20-201010
χ3544-44-4-441-21-21-2-121-2-12-120000000000000000000020-20-10144-44-4-441-21-21-2-121-2-12-120000000000000000000020-20-101
χ3644-44-4-441-21-21-2-121-2-12-1200000000000000000000-202010-144-44-4-441-21-21-2-121-2-12-1200000000000000000000-202010-1
χ3744-44-4-44-21-21-212-1-212-12-1000000000000000000020-20-101044-44-4-44-21-21-212-1-212-12-1000000000000000000020-20-1010
χ3844-44-4-44-21-21-212-1-212-12-10000000000000000000-202010-1044-44-4-44-21-21-212-1-212-12-10000000000000000000-202010-10
χ39888-4-4-4-42-42-4-122-4-12-12-12000000000000000000000000000888-4-4-4-42-42-4-122-4-12-12-12000000000000000000000000000
χ40888-4-4-4-4-42-422-1-422-12-12-1000000000000000000000000000888-4-4-4-4-42-422-1-422-12-12-1000000000000000000000000000
χ4188-8-444-42-42-4-12-24-121-21-200000000000000000000000000088-8-444-42-42-4-12-24-121-21-2000000000000000000000000000
χ4288-8-444-4-42-422-14-22-1-21-2100000000000000000000000000088-8-444-4-42-422-14-22-1-21-21000000000000000000000000000
χ438-80800-82-4-242-400-2400000000000000000000000000000008-80800-82-4-242-400-240000000000000000000000000000000
χ448-80800-8-424-2-42004-200000000000000000000000000000008-80800-8-424-2-42004-20000000000000000000000000000000
χ458-80-4−4i34i342-4-24-12001-2−i32i3i3−2i30000000000000000000000000008-80-4−4i34i342-4-24-12001-2−i32i3i3−2i3000000000000000000000000000
χ468-80-4−4i34i34-424-22-100-212i3−i3−2i3i30000000000000000000000000008-80-4−4i34i34-424-22-100-212i3−i3−2i3i3000000000000000000000000000
χ478-80-44i3−4i342-4-24-12001-2i3−2i3−i32i30000000000000000000000000008-80-44i3−4i342-4-24-12001-2i3−2i3−i32i3000000000000000000000000000
χ488-80-44i3−4i34-424-22-100-21−2i3i32i3−i30000000000000000000000000008-80-44i3−4i34-424-22-100-21−2i3i32i3−i3000000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ501111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-11-11-11
χ52111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111-11-11-11-1
χ5311-11-1-11111111-1-111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11-111-1-1-1-1-1-1-111-1-1111111-1-1-11111-1-1-1-1-1-11111-1-111-1-111
χ5411-11-1-11111111-1-111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11-111-1-1-1-1-1-1-111-1-1111111-1-1-11111-1-1-1-1-1-1111111-1-111-1-1
χ5511-11-1-11111111-1-111-1-1-1-1-1-11-1-111-1-111-1-1-1-111111-1-111-1-11-1-11-111-1-1-1-1-1-1-111-1-1111111-111-1-111-1-11111-1-1-1-1-111-1-111-1
χ5611-11-1-11111111-1-111-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-111-1-111-1-1-11-111-1-1-1-1-1-1-111-1-1111111-111-1-111-1-11111-1-1-1-11-1-111-1-11
χ57222222222222222222222-2-2-20000-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222000022220000000000000000
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χ59222-1-1-1-12222-1-122-1-1-1-1-1-1222-2-2-2-2-1-1-1-11111111100000000-2-2-21111-2-2-2-211-2-2111111-2-2-222221111-1-1-1-1-1-1-1-100000000
χ60222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-20000111133−3−333−3−300000000-2-2-21111-2-2-2-211-2-21111112220000-1-1-1-1−3−333−3−33300000000
χ61222-1-1-1-12222-1-122-1-1-1-1-1-1-2-2-200001111−3−333−3−33300000000-2-2-21111-2-2-2-211-2-21111112220000-1-1-1-133−3−333−3−300000000
χ6222-22-2-22222222-2-222-2-2-2-222-2000022-2-20000000000000000-2-22-222-2-2-2-2-2-2-222-2-22222-2-220000-2-2220000000000000000
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χ6422-2-111-12222-1-1-2-2-1-1111122-20000-1-111−3−33333−3−300000000-2-221-1-11-2-2-2-2112211-1-1-1-1-2-22000011-1-133−3−3−3−33300000000
χ6522-2-111-12222-1-1-2-2-1-11111-2-2222-2-211-1-1-1-1-1-1111100000000-2-221-1-11-2-2-2-2112211-1-1-1-122-2-2-222-1-1111111-1-1-1-100000000
χ6622-2-111-12222-1-1-2-2-1-11111-2-22-2-22211-1-11111-1-1-1-100000000-2-221-1-11-2-2-2-2112211-1-1-1-122-222-2-2-1-111-1-1-1-1111100000000
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χ722-20-1−i3i3122-2-2-1-10011−i3−i3i3i32i−2i0−22i2−i2−ii3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000-2201i3−i3-1-2-2221100-1-1i3i3−i3−i3−2i2i02−2−i2i2i−i−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
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χ752-20-1i3−i3122-2-2-1-10011i3i3−i3−i32i−2i02−2−i2i2−ii−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000-2201−i3i3-1-2-2221100-1-1−i3−i3i3i3−2i2i0−22i2−i2i−i3−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ762-20-1i3−i3122-2-2-1-10011i3i3−i3−i32i−2i0−22i2−i2−ii−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000-2201−i3i3-1-2-2221100-1-1−i3−i3i3i3−2i2i02−2−i2i2i−i3−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ772-20-1i3−i3122-2-2-1-10011i3i3−i3−i3−2i2i02−2i2−i2i−i3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000-2201−i3i3-1-2-2221100-1-1−i3−i3i3i32i−2i0−22−i2i2−ii−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ782-20-1i3−i3122-2-2-1-10011i3i3−i3−i3−2i2i0−22−i2i2i−i3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000-2201−i3i3-1-2-2221100-1-1−i3−i3i3i32i−2i02−2i2−i2−ii−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ7944444441-21-21-21-21-21-21-2000000000000000000002020-10-1-4-4-4-4-4-4-4-12-12-12-12-12-12-1200000000000000000000-20-20101
χ8044444441-21-21-21-21-21-21-200000000000000000000-20-20101-4-4-4-4-4-4-4-12-12-12-12-12-12-12000000000000000000002020-10-1
χ814444444-21-21-21-21-21-21-2100000000000000000002020-10-10-4-4-4-4-4-4-42-12-12-12-12-12-12-10000000000000000000-20-201010
χ824444444-21-21-21-21-21-21-210000000000000000000-20-201010-4-4-4-4-4-4-42-12-12-12-12-12-12-100000000000000000002020-10-10
χ8344-44-4-441-21-21-2-121-2-12-120000000000000000000020-20-101-4-44-444-4-12-12-121-2-121-21-200000000000000000000-202010-1
χ8444-44-4-441-21-21-2-121-2-12-1200000000000000000000-202010-1-4-44-444-4-12-12-121-2-121-21-20000000000000000000020-20-101
χ8544-44-4-44-21-21-212-1-212-12-1000000000000000000020-20-1010-4-44-444-42-12-12-1-212-1-21-210000000000000000000-202010-10
χ8644-44-4-44-21-21-212-1-212-12-10000000000000000000-202010-10-4-44-444-42-12-12-1-212-1-21-21000000000000000000020-20-1010
χ87888-4-4-4-42-42-4-122-4-12-12-12000000000000000000000000000-8-8-84444-24-241-2-241-21-21-2000000000000000000000000000
χ88888-4-4-4-4-42-422-1-422-12-12-1000000000000000000000000000-8-8-844444-24-2-214-2-21-21-21000000000000000000000000000
χ8988-8-444-42-42-4-12-24-121-21-2000000000000000000000000000-8-884-4-44-24-241-22-41-2-12-12000000000000000000000000000
χ9088-8-444-4-42-422-14-22-1-21-21000000000000000000000000000-8-884-4-444-24-2-21-42-212-12-1000000000000000000000000000
χ918-80800-82-4-242-400-240000000000000000000000000000000-880-8008-242-4-24002-40000000000000000000000000000000
χ928-80800-8-424-2-42004-20000000000000000000000000000000-880-80084-2-424-200-420000000000000000000000000000000
χ938-80-4−4i34i342-4-24-12001-2−i32i3i3−2i3000000000000000000000000000-88044i3−4i3-4-242-41-200-12i3−2i3−i32i3000000000000000000000000000
χ948-80-4−4i34i34-424-22-100-212i3−i3−2i3i3000000000000000000000000000-88044i3−4i3-44-2-42-21002-1−2i3i32i3−i3000000000000000000000000000
χ958-80-44i3−4i342-4-24-12001-2i3−2i3−i32i3000000000000000000000000000-8804−4i34i3-4-242-41-200-12−i32i3i3−2i3000000000000000000000000000
χ968-80-44i3−4i34-424-22-100-21−2i3i32i3−i3000000000000000000000000000-8804−4i34i3-44-2-42-21002-12i3−i3−2i3i3000000000000000000000000000

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