Finite Group Databasebeta

← Group #13150594

Character table — Group #13150594

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11112222222222666666661212121212121212121212121818181818181818181818183636363636363636363636361111222222222266666666121212121212121212121212181818181818181818181818363636363636363636363636
order124423466612121212336612121212366666121212121212888824242424242424242244666612121212224426466612121212666612121212666666121212121212888824242424242424242244666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1
χ611-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111
χ711-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-11111-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-111
χ811-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-11111-111-1-1-11111-1-111-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-11111-111-1-1-11111-1-1
χ9222222222222222-12-122-1-1-12-1-1-1-12-1-1-1-1-1000000000000020200-1-100-1-1222222222222222-12-122-1-1-12-1-1-1-12-1-1-1-1-1000000000000020200-1-100-1-1
χ10222222222222222-12-122-1-1-12-1-1-1-12-1-1-1-1-10000000000000-20-200110011222222222222222-12-122-1-1-12-1-1-1-12-1-1-1-1-10000000000000-20-200110011
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χ1222222222222222-12-12-1-122-1-12-1-1-1-12-1-1-1-1000000000000-20-201100110022222222222222-12-12-1-122-1-12-1-1-1-12-1-1-1-1000000000000-20-2011001100
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χ162222-22-2-2-2222-2-2-12-12-1-122-11-211-11-211-1-10000000000000000−i3i300−i3i3002222-22-2-2-2222-2-2-12-12-1-122-11-211-11-211-1-10000000000000000−i3i300−i3i300
χ172222-22-2-2-2222-2-2-12-12-1-122-11-211-11-211-1-10000000000000000i3−i300i3−i3002222-22-2-2-2222-2-2-12-12-1-122-11-211-11-211-1-10000000000000000i3−i300i3−i300
χ1822-2-222-2222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000022-2-222-2222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000
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χ2122-2-222-2222-2-2-2-2-12-1211-2-2-1-12-1-1-11-211110000000000000000−i3i300i3−i30022-2-222-2222-2-2-2-2-12-1211-2-2-1-12-1-1-11-211110000000000000000−i3i300i3−i300
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χ2322-2-2-222-2-22-2-2222-12-1-2-211-1-2111-12-1-1-111000000000000020-200-1-1001122-2-2-222-2-22-2-2222-12-1-2-211-1-2111-12-1-1-111000000000000020-200-1-10011
χ2422-2-2-222-2-22-2-2222-12-1-2-211-1-2111-12-1-1-1110000000000000-202001100-1-122-2-2-222-2-22-2-2222-12-1-2-211-1-2111-12-1-1-1110000000000000-202001100-1-1
χ2522-2-2-222-2-22-2-222-12-1211-2-2-11-211-1-12-1-11100000000000020-20-1-100110022-2-2-222-2-22-2-222-12-1211-2-2-11-211-1-12-1-11100000000000020-20-1-1001100
χ2622-2-2-222-2-22-2-222-12-1211-2-2-11-211-1-12-1-111000000000000-20201100-1-10022-2-2-222-2-22-2-222-12-1211-2-2-11-211-1-12-1-111000000000000-20201100-1-100
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χ302-2−2i2i02000-2−2i2i0022-2-2−2i2i−2i2i20000-20000−2i2i−22−i2i2−2−222−i2−i2i2i20000000000002-2−2i2i02000-2−2i2i0022-2-2−2i2i−2i2i20000-20000−2i2i−22−i2i2−2−222−i2−i2i2i2000000000000
χ3144444444444444-2-2-2-2-2-2-2-21-2-2111-2-2111100000000000000000000000044444444444444-2-2-2-2-2-2-2-21-2-2111-2-21111000000000000000000000000
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χ4366666-36-3-3-3-3-3-3-3000000000000000000002222-1-1-1-1-1-1-1-100000000000066666-36-3-3-3-3-3-3-3000000000000000000002222-1-1-1-1-1-1-1-1000000000000
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χ4766-6-66-3-6-3-3-333330000000000000000000000003−33−3−33−3300000000000066-6-66-3-6-3-3-333330000000000000000000000003−33−3−33−33000000000000
χ4866-6-66-3-6-3-3-33333000000000000000000000000−33−333−33−300000000000066-6-66-3-6-3-3-33333000000000000000000000000−33−333−33−3000000000000
χ4966-6-6-6-3633-333-3-30000000000000000000022-2-2-1-1-1-1111100000000000066-6-6-6-3633-333-3-30000000000000000000022-2-2-1-1-1-11111000000000000
χ5066-6-6-6-3633-333-3-300000000000000000000-2-2221111-1-1-1-100000000000066-6-6-6-3633-333-3-300000000000000000000-2-2221111-1-1-1-1000000000000
χ516-66i−6i0-30−3i33i33−3i3i33−33000000000000000000002−2−i2i2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ70000000000006-66i−6i0-30−3i33i33−3i3i33−33000000000000000000002−2−i2i2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ526-66i−6i0-30−3i33i33−3i3i33−3300000000000000000000−22i2−i2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ70000000000006-66i−6i0-30−3i33i33−3i3i33−3300000000000000000000−22i2−i2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
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χ601111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-111
χ621111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-11-111-1-111-1-1
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χ6611-1-1-111-1-11-1-1111111-1-1-1-11-1-1-1-111111-1-1-1-111-1-1-1-11111-111-1-1-11111-1-1-1-1111-1-111-111-1-1-1-1-1-11111-11111-1-1-1-1-11111-1-11111-1-1-1-11-1-1111-1-1-1-111
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χ7022222222222222-12-12-1-122-1-12-1-1-1-12-1-1-1-1000000000000-20-2011001100-2-2-2-2-2-2-2-2-2-2-2-2-2-21-21-211-2-211-21111-211110000000000002020-1-100-1-100
χ712222-22-2-2-2222-2-2222222222-2-2-2-22-2-2-2-222000000000000000000000000-2-2-2-22-2222-2-2-222-2-2-2-2-2-2-2-2-22222-22222-2-2000000000000000000000000
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χ1096-66i−6i0-30−3i33i33−3i3i33−33000000000000000000002−2−i2i2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000-66−6i6i0303i3−3i3-33i−3i−333300000000000000000000−22i2−i2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000
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χ1136-6−6i6i0-30−3i33i333i−3i−3333000000000000000000002−2i2−i2ζ13−ζ23ζ5−ζ7−ζ13+ζ23−ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ5+ζ7ζ13+ζ23000000000000-666i−6i0303i3−3i3-3−3i3i33−3300000000000000000000−22−i2i2−ζ13+ζ23−ζ5+ζ7ζ13−ζ23ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ5−ζ7−ζ13−ζ23000000000000
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χ1156-6−6i6i0-303i3−3i333i−3i33−33000000000000000000002−2i2−i2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000-666i−6i030−3i33i3-3−3i3i−333300000000000000000000−22−i2i2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000
χ1166-6−6i6i0-303i3−3i333i−3i33−3300000000000000000000−22−i2i2−ζ5+ζ7−ζ13+ζ23ζ5−ζ7ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ13−ζ23−ζ5−ζ7000000000000-666i−6i030−3i33i3-3−3i3i−3333000000000000000000002−2i2−i2ζ5−ζ7ζ13−ζ23−ζ5+ζ7−ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ13+ζ23ζ5+ζ7000000000000

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