Finite Group Databasebeta

← Group #13169432

Character table — Group #13169432

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222224444444444444444448888888888888812121212121218181818181824242424242424242424242424242424242424242424242436363636363636363636363636363654545454
order12223334466666666633366666666612121212121236661212121212121212121244444444444412121212121212121212121212121212121212121212121224466121212121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-111-111-1-1-1-11111-1-111-1-1111111-1-11111-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-111-11-1-111-1-11-11-1111-1111-111-1-11111-1-111-11-1-1-111-1-111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1111-11-1-1-11-1-1-11-111-1-1-1-111-1-1-1-1-1-11-1-1-1-111-1-111-1-11111
χ511111111111111111111111111111111111111111111111111-111-111-1-1-1-111-11-1111-1111-11-1-11111-1-11111-1-11-1-1-1-111-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111-11-1-11-1-1-111-1-1-11-11-1-1-11-1-1-11-1-111-1-1-1-111-1-1-11-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-111-1-11111-1-1-1-11111-1-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-11111111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ111111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-111-111-111-11-1-11-1-1-111-1-111-1-11111-11111-1-1-1-111-1-1-1-111
χ121111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-111-1-1-1-11111-1-1-1111111-1-1-1-11-1111-1-11111-1-1-1-111-1-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-1-11111-1-1-1-1111-1-1-1-1-1-111111-1111-1-11111-1-1-1-1-1-111
χ141111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1111-1-11-1-11-111-1111-1-111-1-111-1-111-11111-1-1-1-111-1-111-1-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
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χ19222222-122-1-1222222-12-1-12-1-12-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-220-220-2-200001-1-2200-22001-111-1-10011-1-100-2001100000000110000
χ20222222-122-1-1222222-12-1-12-1-12-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-20-2-2022000011-2-200-2-20011111100111100200-1-100000000-1-10000
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χ23222222-1-2-2-1-1222222-12-1-12-1-12-1-12-1-1-2-2-2-211-1-1-1-1-2-211111111-2202-20-2-20000-11-22002-2001-1-1-1110011-1-100200-1-100000000110000
χ24222222-1-2-2-1-1222222-12-1-12-1-12-1-12-1-1-2-2-2-211-1-1-1-1-2-211111111-2-20220220000-1-1-2-200220011-1-1-1-100111100-2001100000000-1-10000
χ2522222-1222222-12-12-12-12-1-12-1-12-1-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1022022000022020-12-10-12-10200-1-1-1-100-1-1-1-10020000-1-100-1-1000000
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χ2722222-1222222-12-12-12-12-1-12-1-12-1-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-10-220-220000-2-20-2012-1012-10-20011-1-10011-1-100-20000110011000000
χ2822222-1222222-12-12-12-12-1-12-1-12-1-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-10-2-20-2-20000220-201-2101-210-20011110011110020000-1-100-1-1000000
χ2922222-12-2-2222-12-12-12-12-1-12-1-12-1-12-1-2-211-2-2-1-1-1-111-2-21111110220-2-20000-2-20-20-12-101-210200111100-1-1-1-10020000-1-10011000000
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χ352222-1222222-12-12-122-1-12-1-12-1-12-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-202-20200-2-200-2010-1210-12-201100-1-11100-1-10-200011001100000000
χ362222-1222222-12-12-122-1-12-1-12-1-12-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-20-2-20-2002200-20101-2101-2-2011001111001102000-1-100-1-100000000
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χ4122-2-222200-2-222-2-2-2-22222-2-2-2-2-2-22220000002-2-2200000000000000002-22i−2i2i−2i0000000000000000000000000000000002i−2i2i−2i2-20000
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χ9688-8-8-4-4800-8-8-4-4444482-4-4-244-2442-4-40000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-40044-4-44444-4222-2-2-2-2-2-2222000000-111-1000000−3i33i3−3i33i30000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-40044-4-44444-4222-2-2-2-2-2-2222000000-111-10000003i3−3i33i3−3i30000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-48i−8i4-44444-4-44222-2-2-2222-2-2-2−4i4i−4i4i−4i4i-1-1112i−2i2i−2i2i−2i−i−iii0000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4−8i8i4-44444-4-44222-2-2-2222-2-2-24i−4i4i−4i4i−4i-1-111−2i2i−2i2i−2i2iii−i−i0000000000000000000000000000000000000000000000000000000
χ1018-8-888-4-400-44-848-4-844-4-42-4-4244-244-20000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-400-444-8-484-84-42-4-42-44-244-240000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-48008-844-4-444-82-4-42-4-4-244-2440000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-400-4444-4-4444222222-2-2-2-2-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-400-4444-4-4444222222-2-2-2-2-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).