Finite Group Databasebeta

← Group #13178468

Character table — Group #13178468

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444444444488888888888888888888816161616161616161616181818181818181818181818363636363636363636363636363636363636727272727272
order123334666882233333666661212122424242424246666661212121212242424242424242424246666666666222444666612122222446888121224242424242466661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-1-11-1-11-111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-11-1-11-1-1-111-1-1-1-111-1-1-1-11-1-11-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-1-111-1-1-1-111
χ511111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ611111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-11111-11-1-11-111-1-1-1-1-1-11111
χ711111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-111-1-11-1-11-1-111-1-111-1-111
χ811111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-11-1-11-1-1-1-1-1-1111111-1-1
χ9111111111-1-11-11111111111111-1-1-1-1-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111111111111-11-11-11-1-1-111-1-1-1-1-1-11-11-11-1
χ10111111111-1-11-11111111111111-1-1-1-1-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-1-11-1-111-1-1-1-11-1-11-11-1-1111-1-1-111111-1-11-11
χ11111111111-1-11-11111111111111-1-1-1-1-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11-1-1-111-1-1-111-1-11-11-11-1111-1-111-111-1-11
χ12111111111-1-11-11111111111111-1-1-1-1-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-11-1-1-1-111-11-111-1111-1-1-11111-1-1-11-111-1
χ13111111111-1-1-111111111111111-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-11-111-1-1-111-1-1-1-1-1-1-11-11-11
χ14111111111-1-1-111111111111111-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-1-1-1-1-111-11-1-1-1111-1-1-11111-111-11-1
χ15111111111-1-1-111111111111111-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-111-1-11-1-111-1-11-11-1111-1-1111-1-111-1
χ16111111111-1-1-111111111111111-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11-1-1-1-1111-11-1-11111-1-1-11111-1-11-11-1-11
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χ272222-122-12-2-2-222-1-1-1-12-1-1-1-12-12-2-2-2-211-22-212-12-1-1-1-1-2-211111111-211112-1-1-1-102002000-1-10000-220000-200-1001100001-100
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χ30222-122-1222222-12-1-1-1-12-1-1-1-12222-1-12222-12-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-1-200-200110000-2-200000-20010110000110000
χ31222-122-12222-2-2-12-1-1-1-12-1-1-1-12222-1-122-2-21-21-2-12-1-1-1-1-122-1-1-1-1-1-11-21111-2111200200-1-10000-2-200000200-10-1-10000110000
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χ3822-122222-12222-1-12-1-1-1-12-1-122-1-1-12222-1-12222-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-100-200-20000110000-2-2100-200000011000011
χ3922-122222-122-2-2-1-12-1-1-1-12-1-122-1-1-1222211-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-111-21111-2110020020000-1-10000-2-2-1002000000-1-1000011
χ4022-122222-122-2-2-1-12-1-1-1-12-1-122-1-1-1222211-2-2-2-2-1-12-1-1-1-1-1-122-1-1-1-111-21111-21100-200-2000011000022100-2000000110000-1-1
χ4122-122222-1-2-22-2-1-12-1-1-1-12-1-122-111-2-2-2-2-1122-2-2-1-12-1-11111-2-21111-1-12-1-111-2110020020000-1-100002-2-100-2000000110000-11
χ4222-122222-1-2-22-2-1-12-1-1-1-12-1-122-111-2-2-2-2-1122-2-2-1-12-1-11111-2-21111-1-12-1-111-21100-200-20000110000-221002000000-1-100001-1
χ4322-122222-1-2-2-22-1-12-1-1-1-12-1-122-111-2-2-2-21-1-2-222-1-12-1-11111-2-2111111-211-1-12-1-10020020000-1-10000-22-100-20000001100001-1
χ4422-122222-1-2-2-22-1-12-1-1-1-12-1-122-111-2-2-2-21-1-2-222-1-12-1-11111-2-2111111-211-1-12-1-100-200-200001100002-21002000000-1-10000-11
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χ978-8-4-4-4044442−4200222−1+3i3−1−3i3-2-2-21−3i31+3i3000−2222−2222−2222000000000002−22−22−22ζ5+ζ7−ζ13−2ζ23−2ζ5−ζ7+ζ13+2ζ23−ζ5−2ζ7+2ζ13+ζ23ζ5+2ζ7−2ζ13−ζ230000000000000000000000000000000000000000000000
χ988-8-4-4-40444−424200222−1−3i3−1+3i3-2-2-21+3i31−3i300022−2222−2222−2200000000000−22−22−22ζ5+2ζ7−2ζ13−ζ23−ζ5−2ζ7+2ζ13+ζ23−2ζ5−ζ7+ζ13+2ζ232ζ5+ζ7−ζ13−2ζ230000000000000000000000000000000000000000000000
χ998-8-4-4-40444−424200222−1+3i3−1−3i3-2-2-21−3i31+3i300022−2222−2222−2200000000000−22−22−22−2ζ5−ζ7+ζ13+2ζ232ζ5+ζ7−ζ13−2ζ23ζ5+2ζ7−2ζ13−ζ23−ζ5−2ζ7+2ζ13+ζ230000000000000000000000000000000000000000000000

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