Finite Group Databasebeta

← Group #13178477

Character table — Group #13178477

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444444444488888888888888888888816161616161616161616181818181818181818181818363636363636363636363636363636363636727272727272
order123334666882333334666661212122424242424246661212121212121212242424242424242424246666612121212122224446666121222244468881212242424242424666121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-11-1-11-1-1-11-1-11-111-1-1-1-11-1-11-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-11-1-11-1-1-111-1-1-11-1-11-1-1-11-1-11-1-111-1-1-11-1-11-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-11-1-111-1-11-1-1-1-1-1-111-1-11-1-11
χ511111111111-111111-111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ611111111111-111111-111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-111-111-11-1-11-111-1-1-1-1-111-111
χ711111111111-111111-111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-11-111-11-1-11-1-11-1-111-1-11-111-11
χ811111111111-111111-111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-111-11-1-11-1-1-1-1-1-11111-111-1
χ9111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111111111111111-1-1-111-1-1-111-1-1-1-1-1-111-1-1-11
χ10111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-1-11-1-111-1-1-1-11-11-11-1-1-1111-1-1-111111-11-11-1
χ11111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11-1-1-111-1-1-1111-1-1-11-11-1111-1-111-1111-1-1
χ12111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1111111-1-1-11111-1-1-1-1-1111
χ13111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111-11-1-1-111-1-1-1-1-1-1-1-1111-1
χ14111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-1-1-1-1-11-11-11-1-1111-1-1-11111-11-11-11
χ15111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-111-1-11-1-1-111-11-11-1111-1-1111-1-1-111
χ16111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11-1-1-1-111111-1-1-1111-1-1-11111-1-1111-1-1-1
χ1722222-222200022222022222-2-2-2000000000000-2-2-2-2-20000000000000000000022-2-2-22222222000000-2000-2-2000000000000
χ1822222-222200022222022222-2-2-2000000000000-2-2-2-2-2000000000000000000002-22-22-222-2-2-2-20000002000-22000000000000
χ1922222-222200022222022222-2-2-2000000000000-2-2-2-2-200000000000000000000-2222-2-2-2-222-2-200000020002-2000000000000
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χ282222-1222-1-2-2-22-1-1-1-122-1-1-1-122-1-2-2-2-211-2-2122-12-1-1-1-1-2-211111111-211112-1-1-1-100-200-200001100-20021002000000-1-100100-1
χ29222-1222-12222-12-1-1-12-12-1-1-12-1222-1-1222-122-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-102002000-1-10002002000200-100-1-1000-100-10
χ30222-1222-12222-12-1-1-12-12-1-1-12-1222-1-1222-122-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-10-200-200011000-200-2000-2001001100010010
χ31222-1222-1222-2-12-1-1-1-2-12-1-1-12-1222-1-122-21-2-21-2-12-1-1-1-1-122-1-1-1-1-1-11-21111-211102002000-1-1000-200-2000200-100-1-100010010
χ32222-1222-1222-2-12-1-1-1-2-12-1-1-12-1222-1-122-21-2-21-2-12-1-1-1-1-122-1-1-1-1-1-11-21111-21110-200-2000110002002000-20010011000-100-10
χ33222-1222-12-2-22-12-1-1-1-2-12-1-1-12-12-2-211-2-22-12-21-2-12-1-1-111-2-2111111-12-1-1-11-211102002000-1-1000200-2000-200-10011000-10010
χ34222-1222-12-2-22-12-1-1-1-2-12-1-1-12-12-2-211-2-22-12-21-2-12-1-1-111-2-2111111-12-1-1-11-21110-200-200011000-2002000200100-1-1000100-10
χ35222-1222-12-2-2-2-12-1-1-12-12-1-1-12-12-2-211-2-2-21-22-12-12-1-1-111-2-21111111-2111-12-1-1-102002000-1-1000-2002000-200-10011000100-10
χ36222-1222-12-2-2-2-12-1-1-12-12-1-1-12-12-2-211-2-2-21-22-12-12-1-1-111-2-21111111-2111-12-1-1-10-200-200011000200-2000200100-1-1000-10010
χ3722-1222-122222-1-12-1-12-1-12-1-1-122-1-12222-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-1200200-1-100002002000200-10-1-10000-100-100
χ3822-1222-122222-1-12-1-12-1-12-1-1-122-1-12222-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-1-200-200110000-200-2000-20010110000100100
χ3922-1222-12222-2-1-12-1-1-2-1-12-1-1-122-1-122221-2-21-2-2-1-12-1-1-1-1-1-122-1-1-1-111-21111-211200200-1-10000-200-2000200-10-1-10000100100
χ4022-1222-12222-2-1-12-1-1-2-1-12-1-1-122-1-122221-2-21-2-2-1-12-1-1-1-1-1-122-1-1-1-111-21111-211-200-2001100002002000-20010110000-100-100
χ4122-1222-122-2-22-1-12-1-1-2-1-12-1-1-12211-2-2-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-111-211200200-1-10000200-2000-200-10110000-100100
χ4222-1222-122-2-22-1-12-1-1-2-1-12-1-1-12211-2-2-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-111-211-200-200110000-200200020010-1-10000100-100
χ4322-1222-122-2-2-2-1-12-1-12-1-12-1-1-12211-2-2-2-21-2-2-122-1-12-1-11111-2-2111111-211-1-12-1-1200200-1-10000-2002000-200-10110000100-100
χ4422-1222-122-2-2-2-1-12-1-12-1-12-1-1-12211-2-2-2-21-2-2-122-1-12-1-11111-2-2111111-211-1-12-1-1-200-200110000200-200020010-1-10000-100100
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χ52444-2-244-2-2-4-4-4-2-21114-2-21114-2-2-4-42222-4224-2-2-2-21112222-1-1-1-1-1-122-1-1-1-2-2111000000000000000000000000000000000000
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χ5644-24-24-24-244-4-21-211-4-21-211-24-2-2-244-2-22-422-42-21-211-2-211-2-211112-12-1-12-12-1-1000000000000000000000000000000000000
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χ5844-24-24-24-2-4-4-4-21-2114-21-211-24-222-4-4222-42-24-2-21-21122-1-122-1-1-1-12-12-1-1-21-211000000000000000000000000000000000000
χ5944-2-244-2-244441-2-21141-2-211-2-24-2-2-2-244-2-24-2-241-2-21111-2-2-2-211111-2-2111-2-211000000000000000000000000000000000000
χ6044-2-244-2-2444-41-2-211-41-2-211-2-24-2-2-2-24422-422-41-2-21111-2-2-2-21111-122-1-1-122-1-1000000000000000000000000000000000000
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χ6344-2-2-24-2-2-2444111−1−3i32−1+3i324111−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32000000000000000000000000000000000000
χ6444-2-2-24-2-2-2444111−1+3i32−1−3i324111−1+3i32−1−3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32000000000000000000000000000000000000
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χ918-88-4-40-8444i2−4i20-4-4222044-2-2-20004i2−4i2−2i22i2−2i22i200000000000−2i22i2−2i22i2i2−i2i2−i2i2−i20000000000000000000000000000000000000000000000
χ928-8-48-404-84−4i24i20-42-42204-24-2-20002i2−2i2−4i24i22i2−2i2000000000002i2−2i2−i2i22i2−2i2−i2i2−i2i20000000000000000000000000000000000000000000000
χ938-8-48-404-844i2−4i20-42-42204-24-2-2000−2i22i24i2−4i2−2i22i200000000000−2i22i2i2−i2−2i22i2i2−i2i2−i20000000000000000000000000000000000000000000000
χ948-8-4-48044-8−4i24i202-4-4220-244-2-20002i2−2i22i2−2i2−4i24i200000000000−i2i22i2−2i22i2−2i2−i2i2−i2i20000000000000000000000000000000000000000000000
χ958-8-4-48044-84i2−4i202-4-4220-244-2-2000−2i22i2−2i22i24i2−4i200000000000i2−i2−2i22i2−2i22i2i2−i2i2−i20000000000000000000000000000000000000000000000
χ968-8-4-4-40444−4i24i20222−1−3i3−1+3i30-2-2-21+3i31−3i30002i2−2i22i2−2i22i2−2i200000000000−i2i2−i2i2−i2i2−ζ5+2ζ7+2ζ13−ζ23ζ5−2ζ7−2ζ13+ζ232ζ5−ζ7−ζ13+2ζ23−2ζ5+ζ7+ζ13−2ζ230000000000000000000000000000000000000000000000
χ978-8-4-4-40444−4i24i20222−1+3i3−1−3i30-2-2-21−3i31+3i30002i2−2i22i2−2i22i2−2i200000000000−i2i2−i2i2−i2i22ζ5−ζ7−ζ13+2ζ23−2ζ5+ζ7+ζ13−2ζ23−ζ5+2ζ7+2ζ13−ζ23ζ5−2ζ7−2ζ13+ζ230000000000000000000000000000000000000000000000
χ988-8-4-4-404444i2−4i20222−1−3i3−1+3i30-2-2-21+3i31−3i3000−2i22i2−2i22i2−2i22i200000000000i2−i2i2−i2i2−i2ζ5−2ζ7−2ζ13+ζ23−ζ5+2ζ7+2ζ13−ζ23−2ζ5+ζ7+ζ13−2ζ232ζ5−ζ7−ζ13+2ζ230000000000000000000000000000000000000000000000
χ998-8-4-4-404444i2−4i20222−1+3i3−1−3i30-2-2-21−3i31+3i3000−2i22i2−2i22i2−2i22i200000000000i2−i2i2−i2i2−i2−2ζ5+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.