Finite Group Databasebeta

← Group #13167833

Character table — Group #13167833

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222224444444444444444444446666668888888888888812121212121212121212121212121212121212181818182424242424242424363636363636363648484848545472727272108
order1233346668833366612121212122424242424242424242424661212361212121224242424242424242244666812121224242424242424242412126666121212122244682424661212246612128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-11-1111111111111111-1-1-1-11-11-11-11-11-11-1-1-1-1-11-11-1-1-11-11-1-1
χ31111111111111111111111111111111111111111111111111111-11-11111111111111111-1-1-1-1-11-11-11-11-11-11-1-1-1-1-11-11-1-1-11-11-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ511111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1-11-11-1-1-1-11-11-111-11-111
χ711111111111111111111111111111111-1-1-1-1-1-111111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-111-11-1-1-1-1-1-11-11111-11-11
χ811111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1
χ9111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1111-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-111111-1-1-1-11-1-111
χ10111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-111111-11-1-11-1111-1-11-1-1-11-1-111111-1-1-1
χ11111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1111-1111-1-1-1-1-1-1-1-11111-11-111-11-1-1-1111-1-1-1-111-111-1-111-1
χ12111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1111-1-111-1-1-111-11
χ13111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-111111-1-111-111-1-1
χ14111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-11-1-1-11111111111111-11-1-11-11-1-1111-1-1-11-1-11-1-1-1-1111
χ15111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1111111111111-11-111-11-111-1-11-1-1-1-111-1-1-111-1-11
χ16111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1111-1-111111-1-11-1
χ1722222-222200222222-2-2-2-2-200000000002-222-2-222-2-2-2-20000000000002220-2-2-2000000002-2-2-200000000000020000000-2200000
χ1822222-222200222222-2-2-2-2-200000000002-222-2-222-2-2-2-20000000000002220-2-2-200000000-2222000000000000-200000002-200000
χ1922222-222200222222-2-2-2-2-20000000000-22-2-22222-2-2-2-2000000000000-2-2-20222000000002-2-2-2000000000000200000002-200000
χ2022222-222200222222-2-2-2-2-20000000000-22-2-22222-2-2-2-2000000000000-2-2-2022200000000-2222000000000000-20000000-2200000
χ212222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-1222222-1-1-1-12-1-1-122-1-1-1-1-1-10202-1-1-122-1-122-1-1-1-1-1-10000020-1020-1020200000-10-1000-10-10
χ222222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-1222222-1-1-1-12-1-1-122-1-1-1-1-1-10-20-2-1-1-122-1-122-1-1-1-1-1-100000-2010-2010-20-2000001010001010
χ232222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-122-2-2-2-211-1-12-1-1-122-1-1-1-1-1-10202111-2-211-2-21111110000020-1020-10-20-200000-10-10001010
χ242222-1222-122-12-1-12-12-1-1-1222-1-1-1-1-1-122-2-2-2-211-1-12-1-1-122-1-1-1-1-1-10-20-2111-2-211-2-211111100000-2010-201020200000101000-10-10
χ252222-1222-1-2-2-12-1-12-12-1-1-12-2-2111111-2-22222-1-1-1-12-1-1-1-2-2111111020-2-1-1-1-22-1-1-2-21111110000020-10-2010-20200000-10100010-10
χ262222-1222-1-2-2-12-1-12-12-1-1-12-2-2111111-2-22222-1-1-1-12-1-1-1-2-21111110-202-1-1-1-22-1-1-2-211111100000-201020-1020-20000010-1000-1010
χ272222-1222-1-2-2-12-1-12-12-1-1-12-2-2111111-2-2-2-2-2-211-1-12-1-1-1-2-2111111020-21112-21122-1-1-1-1-1-10000020-10-201020-200000-101000-1010
χ282222-1222-1-2-2-12-1-12-12-1-1-12-2-2111111-2-2-2-2-2-211-1-12-1-1-1-2-21111110-2021112-21122-1-1-1-1-1-100000-201020-10-2020000010-100010-10
χ29222-1222-1222-1-12-1-12-12-1-12-1-122-1-1-1-12222-1-122-1-1-12-1-1-1-122-1-1-1-120202-1-12-1-1-1-1-122-1-1-1-1000020-1020-1020200000-10-1000-10-100
χ30222-1222-1222-1-12-1-12-12-1-12-1-122-1-1-1-12222-1-122-1-1-12-1-1-1-122-1-1-1-1-20-202-1-12-1-1-1-1-122-1-1-1-10000-2010-2010-20-20000010100010100
χ31222-1222-1222-1-12-1-12-12-1-12-1-122-1-1-1-122-2-211-2-2-1-1-12-1-1-1-122-1-1-1-12020-211-211111-2-21111000020-1020-10-20-200000-10-100010100
χ32222-1222-1222-1-12-1-12-12-1-12-1-122-1-1-1-122-2-211-2-2-1-1-12-1-1-1-122-1-1-1-1-20-20-211-211111-2-211110000-2010-201020200000101000-10-100
χ33222-1222-12-2-2-1-12-1-12-12-1-1211-2-21111-2-222-1-122-1-1-12-1-111-2-2111120-202-1-1-2-1-1-111-2-21111000020-10-201020-200000-101000-10100
χ34222-1222-12-2-2-1-12-1-12-12-1-1211-2-21111-2-222-1-122-1-1-12-1-111-2-21111-20202-1-1-2-1-1-111-2-211110000-201020-10-2020000010-100010-100
χ35222-1222-12-2-2-1-12-1-12-12-1-1211-2-21111-2-2-2-211-2-2-1-1-12-1-111-2-2111120-20-2112111-1-122-1-1-1-1000020-10-2010-20200000-10100010-100
χ36222-1222-12-2-2-1-12-1-12-12-1-1211-2-21111-2-2-2-211-2-2-1-1-12-1-111-2-21111-2020-2112111-1-122-1-1-1-10000-201020-1020-20000010-1000-10100
χ3722-1222-122222-1-12-1-12222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000022-1-1-1-122-1-1220000-12-1-1-1-1-1-10000000
χ3822-1222-122222-1-12-1-12222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-12-22-2000000000000000-2-211-112-2-112-200001-211-11-110000000
χ3922-1222-122222-1-12-1-12222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-22000000000000000-2-2111-1-221-1-2200001-2111-11-10000000
χ4022-1222-122222-1-12-1-12222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000022-1-111-2-211-2-20000-12-1-111110000000
χ4122-1222-122-2-22-1-12-1-12222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-11111111122-2-2000000000000000-2-211-1-12211-2-2000012-1-1-1-1110000000
χ4222-1222-122-2-22-1-12-1-12222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-1111111112-2-2200000000000000022-1-1-112-21-1-220000-1-211-111-10000000
χ4322-1222-122-2-22-1-12-1-12222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-111111111-222-200000000000000022-1-11-1-22-112-20000-1-2111-1-110000000
χ4422-1222-122-2-22-1-12-1-12222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-111111111-2-222000000000000000-2-21111-2-2-1-122000012-1-111-1-10000000
χ454444-2-444-200-24-2-24-2-4222-400000000004-44422-2-2-4222000000000000-2-2-20-422000000000000000000000000000000000000000
χ464444-2-444-200-24-2-24-2-4222-40000000000-44-4-4-2-2-2-2-422200000000000022204-2-2000000000000000000000000000000000000000
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χ50444-2-244-2-2441-2-21-2-2-2-2114-2-2-2-2111144-4-4222211-2-211-2-2-2-2111100002-1-1-42-1-12222-1-1-1-10000000000000000000000000000000
χ51444-2-244-2-2-4-41-2-21-2-2-2-21142222-1-1-1-1-4-444-2-2-2-211-2-2112222-1-1-1-10000-211-4-2112222-1-1-1-10000000000000000000000000000000
χ52444-2-244-2-2-4-41-2-21-2-2-2-21142222-1-1-1-1-4-4-4-4222211-2-2112222-1-1-1-100002-1-142-1-1-2-2-2-211110000000000000000000000000000000
χ53444-2-2-44-2-2001-2-21-2-222-1-1-400003i3i−3i−3i004-4-2-2221122-1-100003i3i−3i−3i0000-21102-1-100003i3i−3i−3i0000000000000000000000000000000
χ54444-2-2-44-2-2001-2-21-2-222-1-1-400003i3i−3i−3i00-4422-2-21122-1-100003i3i−3i−3i00002-1-10-2110000−3i−3i3i3i0000000000000000000000000000000
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χ56444-2-2-44-2-2001-2-21-2-222-1-1-40000−3i−3i3i3i00-4422-2-21122-1-10000−3i−3i3i3i00002-1-10-21100003i3i−3i−3i0000000000000000000000000000000
χ5744-244-4-244004-2-24-2-2-4-4-4-420000000000000000-2-222220000000000000000000000000004-422000000000000-200000000000000
χ5844-244-4-244004-2-24-2-2-4-4-4-420000000000000000-2-22222000000000000000000000000000-44-2-2000000000000200000000000000
χ5944-24-24-24-244-2-21-2-214-2-2-2-244-2-2-2-2-2-2-2-200000011-2111-2-2111111040400000000000000000000-20-20-20-20000000001010000000
χ6044-24-24-24-244-2-21-2-214-2-2-2-244-2-2-2-2-2-2-2-200000011-2111-2-21111110-40-4000000000000000000002020202000000000-10-10000000
χ6144-24-24-24-2-4-4-2-21-2-214-2-2-2-2-4-42222222200000011-211122-1-1-1-1-1-1040-400000000000000000000-20-2020200000000010-10000000
χ6244-24-24-24-2-4-4-2-21-2-214-2-2-2-2-4-42222222200000011-211122-1-1-1-1-1-10-404000000000000000000002020-20-2000000000-1010000000
χ6344-2-244-2-2444-21-2-21-2-24-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-2111140400000000000000000000-20-20-20-200000000010100000000
χ6444-2-244-2-2444-21-2-21-2-24-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-21111-40-4000000000000000000002020202000000000-10-100000000
χ6544-2-244-2-24-4-4-21-2-21-2-24-2-2-222-4-4222222000000111-211-1-122-1-1-1-140-400000000000000000000-20-2020200000000010-100000000
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χ1018-8-4-4-404444i2−4i2222-2-2-2006i−6i0−2i22i2−2i22i24ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ23−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ23−2i22i2000000-1100−3i3ii2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000000000000000000000000000000000000
χ1028-8-4-4-404444i2−4i2222-2-2-200−6i6i0−2i22i2−2i22i2−2ζ5+4ζ7−2ζ13+4ζ232ζ5−4ζ7+2ζ13−4ζ234ζ5−2ζ7+4ζ13−2ζ23−4ζ5+2ζ7−4ζ13+2ζ23−2i22i2000000-11003i−3ii2−i2i2−i2ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ2300000000000000000000000000000000000000000000000000

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