Finite Group Databasebeta

← Group #13178471

Character table — Group #13178471

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444444444488888888888888888888816161616161616161616181818181818181818181818363636363636363636363636363636363636727272727272
order123334666882233333666661212122424242424246666661212121212242424242424242424246666666666222444121212121212444444666888242424242424121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-11-1-11-1-1-111-1-1-1-111-1-1-11-1-11-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-111-1-11-1-11-1-1-1-111-1-1-1-111
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
χ611111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-111111-1-11-1-111-1-1-1-1-1-11111
χ711111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-111-1-111-11-1-11-1-1-111-1-111-1-111
χ811111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1111111-1-1
χ9111111111-1-11-11111111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11111111111111-11-11-1111-1-1-1-1-1-1-1-1-11-11-11-1
χ10111111111-1-11-11111111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-1-11-1-111-1-1-1-11-1-11-111-1-1-111-1-111111-1-11-11
χ11111111111-1-11-11111111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11-1-1-111-1-1-111-1-11-11-11-1111-1-111-111-1-11
χ12111111111-1-11-11111111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-11-1-1-1-111-11-111-1-1-1111-11111-1-1-11-111-1
χ13111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-11-11111-1-1-1-1-1-1-1-1-1-11-11-11
χ14111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-1-1-1-1-111-11-11-1-1-111-1-11111-111-11-1
χ15111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-111-1-11-1-111-1-11-11-1111-1-1111-1-111-1
χ16111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11-1-1-1-1111-11-1-11-1-1111-11111-1-11-11-1-11
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χ212222-1222-122222-1-1-1-12-1-1-1-122-12222-1-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-10020020000-1-100002200-10020000-1-10000-1-1
χ222222-1222-122222-1-1-1-12-1-1-1-122-12222-1-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-100-200-20000110000-2-200100-2000011000011
χ232222-1222-122-2-22-1-1-1-12-1-1-1-122-12222-1-1-2-21-2-212-1-1-1-122-1-1-1-1-1-1-1-1-21111-211110020020000-1-10000-2-200-10020000-1-1000011
χ242222-1222-122-2-22-1-1-1-12-1-1-1-122-12222-1-1-2-21-2-212-1-1-1-122-1-1-1-1-1-1-1-1-21111-2111100-200-200001100002200100-20000110000-1-1
χ252222-1222-1-2-22-22-1-1-1-12-1-1-1-122-1-2-2-2-21122-1-2-212-1-1-1-1-2-2111111112-1-1-1-1-211110020020000-1-100002-200-100-20000110000-11
χ262222-1222-1-2-22-22-1-1-1-12-1-1-1-122-1-2-2-2-21122-1-2-212-1-1-1-1-2-2111111112-1-1-1-1-2111100-200-20000110000-220010020000-1-100001-1
χ272222-1222-1-2-2-222-1-1-1-12-1-1-1-122-1-2-2-2-211-2-2122-12-1-1-1-1-2-211111111-211112-1-1-1-10020020000-1-10000-2200-100-200001100001-1
χ282222-1222-1-2-2-222-1-1-1-12-1-1-1-122-1-2-2-2-211-2-2122-12-1-1-1-1-2-211111111-211112-1-1-1-100-200-200001100002-20010020000-1-10000-11
χ29222-1222-122222-12-1-1-1-12-1-1-12-1222-1-1222-122-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-102002000-1-1000022000-1002000-1-10000-1-100
χ30222-1222-122222-12-1-1-1-12-1-1-12-1222-1-1222-122-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-10-200-2000110000-2-2000100-20001100001100
χ31222-1222-1222-2-2-12-1-1-1-12-1-1-12-1222-1-122-21-2-21-2-12-1-1-1-1-122-1-1-1-1-1-11-21111-211102002000-1-10000-2-2000-1002000-1-100001100
χ32222-1222-1222-2-2-12-1-1-1-12-1-1-12-1222-1-122-21-2-21-2-12-1-1-1-1-122-1-1-1-1-1-11-21111-21110-200-200011000022000100-2000110000-1-100
χ33222-1222-12-2-22-2-12-1-1-1-12-1-1-12-12-2-211-2-22-12-21-2-12-1-1-111-2-2111111-12-1-1-11-211102002000-1-100002-2000-100-2000110000-1100
χ34222-1222-12-2-22-2-12-1-1-1-12-1-1-12-12-2-211-2-22-12-21-2-12-1-1-111-2-2111111-12-1-1-11-21110-200-2000110000-220001002000-1-100001-100
χ35222-1222-12-2-2-22-12-1-1-1-12-1-1-12-12-2-211-2-2-21-22-12-12-1-1-111-2-21111111-2111-12-1-1-102002000-1-10000-22000-100-20001100001-100
χ36222-1222-12-2-2-22-12-1-1-1-12-1-1-12-12-2-211-2-2-21-22-12-12-1-1-111-2-21111111-2111-12-1-1-10-200-20001100002-20001002000-1-10000-1100
χ3722-1222-1222222-1-12-1-1-1-12-1-1-122-1-12222-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-1200200-1-10000220000-100200-1-10000-1-10000
χ3822-1222-1222222-1-12-1-1-1-12-1-1-122-1-12222-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-1-200-200110000-2-20000100-200110000110000
χ3922-1222-12222-2-2-1-12-1-1-1-12-1-1-122-1-122221-2-21-2-2-1-12-1-1-1-1-1-122-1-1-1-111-21111-211200200-1-10000-2-20000-100200-1-10000110000
χ4022-1222-12222-2-2-1-12-1-1-1-12-1-1-122-1-122221-2-21-2-2-1-12-1-1-1-1-1-122-1-1-1-111-21111-211-200-200110000220000100-200110000-1-10000
χ4122-1222-122-2-22-2-1-12-1-1-1-12-1-1-12211-2-2-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-111-211200200-1-100002-20000-100-200110000-110000
χ4222-1222-122-2-22-2-1-12-1-1-1-12-1-1-12211-2-2-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-111-211-200-200110000-220000100200-1-100001-10000
χ4322-1222-122-2-2-22-1-12-1-1-1-12-1-1-12211-2-2-2-21-2-2-122-1-12-1-11111-2-2111111-211-1-12-1-1200200-1-10000-220000-100-2001100001-10000
χ4422-1222-122-2-2-22-1-12-1-1-1-12-1-1-12211-2-2-2-21-2-2-122-1-12-1-11111-2-2111111-211-1-12-1-1-200-2001100002-20000100200-1-10000-110000
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χ5644-24-24-24-244-4-4-21-211-21-211-24-2-2-244-2-22-422-42-21-211-2-211-2-211112-12-1-12-12-1-1000000000000000000000000000000000000
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χ5844-24-24-24-2-4-4-44-21-211-21-211-24-222-4-4222-42-24-2-21-21122-1-122-1-1-1-12-12-1-1-21-211000000000000000000000000000000000000
χ5944-2-244-2-2444441-2-2111-2-211-2-24-2-2-2-244-2-24-2-241-2-21111-2-2-2-211111-2-2111-2-211000000000000000000000000000000000000
χ6044-2-244-2-2444-4-41-2-2111-2-211-2-24-2-2-2-24422-422-41-2-21111-2-2-2-21111-122-1-1-122-1-1000000000000000000000000000000000000
χ6144-2-244-2-24-4-44-41-2-2111-2-211-2-242222-4-4-2-2422-41-2-211-1-12222-1-1-1-11-2-211-122-1-1000000000000000000000000000000000000
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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.