Finite Group Databasebeta

← Group #13167797

Character table — Group #13167797

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222223344444444444444444444466666668888888888888899121212121212121212121212121212121212181818181824242424242424242727363636363636364848484854545472727272
order1233346668844333666121212121224242424242424242424288121212123612121212242424242424242422224466661212242424242424242446688666612121212442244122424661212288661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111-1-11-11-111111111111111-1-1-1-1-11-11-11-11-1-1-11-11-1-1-1-11-11-1-1-1-11-11-1
χ41111111111111111111111111111111111111111111111111111111-1-1-11-1111111111111111-1-1-1-1-1-11-11-11-11-1-1-11-11-1-1-1-11-11-1-1-1-11-11
χ511111111111-1-1111111111111111111111-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1
χ611111111111-1-1111111111111111111111-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111
χ711111111111-1-1111111111111111111111-1-1-1-1-1-1-111111111111111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-111-11-11-1-1-11-11-1111-11-11
χ811111111111-1-1111111111111111111111-1-1-1-1-1-1-111111111111111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11111-11-1-1-1-1-11-111111-11-1
χ9111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111-1-1111-1-111-1-11-1-1-1-111
χ10111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-11-1-1-1-1111-1-111-1-1
χ11111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1111-11-1-11-11-1-1-111-1-1111-1-11-111-111-1
χ12111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-111-11-111-11-1-1-11-1-11-111-111-1-1111-1-11
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-11111-1-1-1-1-1-111-1-11-1-111-1-1-11111-1-1
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-111-1-111
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-1-1111-11-1-11-11111-1-11-1111-1-111-1-11-1-11
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-111-11-111-11-111-111-1-111-111-11-1-1-111-1
χ1722222-22220022222222-2-2-2-2-20000000000-200222222-2-2-2-200000000220000-2-2-2-22200000000-2220000000000220000-2000000-2000000
χ1822222-22220022222222-2-2-2-2-20000000000-200222222-2-2-2-200000000-2-20000-2-2-2-222000000002-2-20000000000-2-2000020000002000000
χ1922222-222200-2-2222222-2-2-2-2-20000000000200-2-2-2-222-2-2-2-2000000002200002222-2-200000000-2220000000000-2-20000-20000002000000
χ2022222-222200-2-2222222-2-2-2-2-20000000000200-2-2-2-222-2-2-2-200000000-2-200002222-2-2000000002-2-200000000002200002000000-2000000
χ212222-1222-12222-12-1-12-12-1-1-1222-1-1-1-1-1-12222222-1-1-1-12-1-1-122-1-1-1-1-1-10002022-1-1-1-1-122-1-1-1-1-1-100000020-1020-10002020000-10-10000-10-1
χ222222-1222-12222-12-1-12-12-1-1-1222-1-1-1-1-1-12222222-1-1-1-12-1-1-122-1-1-1-1-1-1000-20-22-1-1-1-1-122-1-1-1-1-1-1000000-2010-201000-20-200001010000101
χ232222-1222-122-2-2-12-1-12-12-1-1-1222-1-1-1-1-1-122-2-2-2-2-211-1-12-1-1-122-1-1-1-1-1-1000202-211111-2-211111100000020-1020-1000-20-20000-10-10000101
χ242222-1222-122-2-2-12-1-12-12-1-1-1222-1-1-1-1-1-122-2-2-2-2-211-1-12-1-1-122-1-1-1-1-1-1000-20-2-211111-2-2111111000000-2010-20100020200001010000-10-1
χ252222-1222-1-2-222-12-1-12-12-1-1-12-2-2111111-2-22-2-222-1-1-1-12-1-1-1-2-211111100020-22-1-1-1-1-1-2-211111100000020-10-201000-2020000-101000010-1
χ262222-1222-1-2-222-12-1-12-12-1-1-12-2-2111111-2-22-2-222-1-1-1-12-1-1-1-2-2111111000-2022-1-1-1-1-1-2-2111111000000-201020-100020-2000010-10000-101
χ272222-1222-1-2-2-2-2-12-1-12-12-1-1-12-2-2111111-2-2-222-2-211-1-12-1-1-1-2-211111100020-2-21111122-1-1-1-1-1-100000020-10-20100020-20000-1010000-101
χ282222-1222-1-2-2-2-2-12-1-12-12-1-1-12-2-2111111-2-2-222-2-211-1-12-1-1-1-2-2111111000-202-21111122-1-1-1-1-1-1000000-201020-1000-202000010-1000010-1
χ29222-1222-122222-1-12-1-12-12-1-12-1-122-1-1-1-122222-1-122-1-1-12-1-1-1-122-1-1-1-1002020-12-1-1-1-1-1-122-1-1-1-10000020-1020-10002020000-10-10000-10-10
χ30222-1222-122222-1-12-1-12-12-1-12-1-122-1-1-1-122222-1-122-1-1-12-1-1-1-122-1-1-1-100-20-20-12-1-1-1-1-1-122-1-1-1-100000-2010-201000-20-2000010100001010
χ31222-1222-1222-2-2-1-12-1-12-12-1-12-1-122-1-1-1-122-2-2-211-2-2-1-1-12-1-1-1-122-1-1-1-10020201-2111111-2-211110000020-1020-1000-20-20000-10-100001010
χ32222-1222-1222-2-2-1-12-1-12-12-1-12-1-122-1-1-1-122-2-2-211-2-2-1-1-12-1-1-1-122-1-1-1-100-20-201-2111111-2-2111100000-2010-20100020200001010000-10-10
χ33222-1222-12-2-222-1-12-1-12-12-1-1211-2-21111-2-22-2-2-1-122-1-1-12-1-111-2-211110020-20-12-1-1-1-111-2-211110000020-10-201000-2020000-101000010-10
χ34222-1222-12-2-222-1-12-1-12-12-1-1211-2-21111-2-22-2-2-1-122-1-1-12-1-111-2-2111100-2020-12-1-1-1-111-2-2111100000-201020-100020-2000010-10000-1010
χ35222-1222-12-2-2-2-2-1-12-1-12-12-1-1211-2-21111-2-2-22211-2-2-1-1-12-1-111-2-211110020-201-21111-1-122-1-1-1-10000020-10-20100020-20000-1010000-1010
χ36222-1222-12-2-2-2-2-1-12-1-12-12-1-1211-2-21111-2-2-22211-2-2-1-1-12-1-111-2-2111100-20201-21111-1-122-1-1-1-100000-201020-1000-202000010-1000010-10
χ3722-1222-12222002-1-12-1-12222-122222222-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222000000000000002-1-122-1-122-1-122000000-1-1-1-1-1-1-10000000
χ3822-1222-12222002-1-12-1-12222-122222222-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2000000000000002-1-12211-2-211-2-2000000-1-1-111110000000
χ3922-1222-12222002-1-12-1-12222-122222222-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22-22-200000000000000-211-2-2-112-2-112-2000000111-11-110000000
χ4022-1222-12222002-1-12-1-12222-122222222-1-10000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-22-2200000000000000-211-2-21-1-221-1-220000001111-11-10000000
χ4122-1222-122-2-2002-1-12-1-12222-1-2-2-2-2-2-2-2-2110000000-1-1-1-1-1-1111111112222-2-2000000000000002-1-1-2-2-1-12211-2-2000000-111-1-1110000000
χ4222-1222-122-2-2002-1-12-1-12222-1-2-2-2-2-2-2-2-2110000000-1-1-1-1-1-11111111122-2-222000000000000002-1-1-2-211-2-2-1-122000000-11111-1-10000000
χ4322-1222-122-2-2002-1-12-1-12222-1-2-2-2-2-2-2-2-2110000000-1-1-1-1-1-111111111-2-22-2-2200000000000000-21122-112-21-1-220000001-1-1-111-10000000
χ4422-1222-122-2-2002-1-12-1-12222-1-2-2-2-2-2-2-2-2110000000-1-1-1-1-1-111111111-2-2-222-200000000000000-211221-1-22-112-20000001-1-11-1-110000000
χ452-22220-2-2-2i2−i22i−2i222-2-2-200000i2−i2i2−i2i2i2−i2−i2i2−i202−22i−2i2i−2i2-20000i2−i2i2−i2i2i2−i2−i22-2000000002i−2i2−22−222−2−202-2i2−i2000000002i−2i00000i2−i2000002−20000
χ462-22220-2-2-2i2−i22i−2i222-2-2-200000i2−i2i2−i2i2i2−i2−i2i2−i202−22i−2i2i−2i2-20000i2−i2i2−i2i2i2−i2−i2-22000000002i−2i2−22−222−2−20-22−i2i200000000−2i2i00000−i2i200000−220000
χ472-22220-2-2-2i2−i2−2i2i222-2-2-200000i2−i2i2−i2i2i2−i2−i2i2−i20−22−2i2i−2i2i2-20000i2−i2i2−i2i2i2−i2−i22-200000000−2i2i−22−22−2−22202-2i2−i200000000−2i2i00000i2−i200000−220000
χ482-22220-2-2-2i2−i2−2i2i222-2-2-200000i2−i2i2−i2i2i2−i2−i2i2−i20−22−2i2i−2i2i2-20000i2−i2i2−i2i2i2−i2−i2-2200000000−2i2i−22−22−2−2220-22−i2i2000000002i−2i00000−i2i2000002−20000
χ492-22220-2-2-2−i2i22i−2i222-2-2-200000−i2i2−i2i2−i2−i2i2i2−i2i20−222i−2i2i−2i2-20000−i2i2−i2i2−i2−i2i2i22-2000000002i−2i−22−22−2−22202-2−i2i2000000002i−2i00000−i2i200000−220000
χ502-22220-2-2-2−i2i22i−2i222-2-2-200000−i2i2−i2i2−i2−i2i2i2−i2i20−222i−2i2i−2i2-20000−i2i2−i2i2−i2−i2i2i2-22000000002i−2i−22−22−2−2220-22i2−i200000000−2i2i00000i2−i2000002−20000
χ512-22220-2-2-2−i2i2−2i2i222-2-2-200000−i2i2−i2i2−i2−i2i2i2−i2i202−2−2i2i−2i2i2-20000−i2i2−i2i2−i2−i2i2i22-200000000−2i2i2−22−222−2−202-2−i2i200000000−2i2i00000−i2i2000002−20000
χ522-22220-2-2-2−i2i2−2i2i222-2-2-200000−i2i2−i2i2−i2−i2i2i2−i2i202−2−2i2i−2i2i2-20000−i2i2−i2i2−i2−i2i2i2-2200000000−2i2i2−22−222−2−20-22i2−i2000000002i−2i00000i2−i200000−220000
χ534444-2-444-20044-24-2-24-2-4222-40000000000-40044-2-2-2-2-422200000000000000-4222-2-200000000000000000000000000000000000000000
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χ57444-2-244-2-244441-2-21-2-2-2-2114-2-2-2-2111144444-2-2-2-211-2-211-2-2-2-21111000000-2-21111-2-2-2-21111000000000000000000000000000000000
χ58444-2-244-2-244-4-41-2-21-2-2-2-2114-2-2-2-2111144-4-4-4222211-2-211-2-2-2-2111100000022-1-1-1-12222-1-1-1-1000000000000000000000000000000000
χ59444-2-244-2-2-4-4441-2-21-2-2-2-21142222-1-1-1-1-4-44-4-4-2-2-2-211-2-2112222-1-1-1-1000000-2-211112222-1-1-1-1000000000000000000000000000000000
χ60444-2-244-2-2-4-4-4-41-2-21-2-2-2-21142222-1-1-1-1-4-4-444222211-2-2112222-1-1-1-100000022-1-1-1-1-2-2-2-21111000000000000000000000000000000000
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χ6544-244-4-24400004-2-24-2-2-4-4-4-4200000000000000000-2-222220000000044000000000000000000-4-2-2000000000000000020000000000000
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χ6844-24-24-24-24400-2-21-2-214-2-2-2-244-2-2-2-2-2-2-2-2000000011-2111-2-2111111000-40-40000000000000000000020202020000000000-10-10000000
χ6944-24-24-24-2-4-400-2-21-2-214-2-2-2-2-4-422222222000000011-211122-1-1-1-1-1-100040-400000000000000000000-20-20202000000000010-10000000
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χ7144-2-244-2-244400-21-2-21-2-24-2-2-2-2-244-2-2-2-2-2-20000000111-21111-2-211110040400000000000000000000-20-20-20-2000000000010100000000
χ7244-2-244-2-244400-21-2-21-2-24-2-2-2-2-244-2-2-2-2-2-20000000111-21111-2-2111100-40-40000000000000000000020202020000000000-10-100000000
χ7344-2-244-2-24-4-400-21-2-21-2-24-2-2-222-4-42222220000000111-211-1-122-1-1-1-10040-400000000000000000000-20-20202000000000010-100000000
χ7444-2-244-2-24-4-400-21-2-21-2-24-2-2-222-4-42222220000000111-211-1-122-1-1-1-100-404000000000000000000002020-20-20000000000-10100000000
χ754-444-20-4-422i2−2i24i−4i-24-22-42000002i2−2i2−i2i2−i2−i2i2i22i2−2i2022−224i−4i−2i2i-2200002i2−2i2−i2i2−i2−i2i2i20000000000−2i2i22−22−22−2−222000000000000000000000000000000000
χ764-444-20-4-422i2−2i2−4i4i-24-22-42000002i2−2i2−i2i2−i2−i2i2i22i2−2i20−2222−4i4i2i−2i-2200002i2−2i2−i2i2−i2−i2i2i200000000002i−2i−22222−222−2−2000000000000000000000000000000000
χ774-444-20-4-42−2i22i24i−4i-24-22-4200000−2i22i2i2−i2i2i2−i2−i2−2i22i20−22224i−4i−2i2i-220000−2i22i2i2−i2i2i2−i2−i20000000000−2i2i−22222−222−2−2000000000000000000000000000000000
χ784-444-20-4-42−2i22i2−4i4i-24-22-4200000−2i22i2i2−i2i2i2−i2−i2−2i22i2022−22−4i4i2i−2i-220000−2i22i2i2−i2i2i2−i2−i200000000002i−2i22−22−22−2−222000000000000000000000000000000000
χ794-44-240-42-42i2−2i24i−4i-2-2422-400000−i2i22i2−2i2−i2−i2i2i22i2−2i2022−22−2i2i4i−4i-220000−i2i22i2−2i2−i2−i2i2i20000000000−2i2i−2222−22−2−222000000000000000000000000000000000
χ804-44-240-42-42i2−2i2−4i4i-2-2422-400000−i2i22i2−2i2−i2−i2i2i22i2−2i20−22222i−2i−4i4i-220000−i2i22i2−2i2−i2−i2i2i200000000002i−2i2−2−222222−2−2000000000000000000000000000000000
χ814-44-240-42-4−2i22i24i−4i-2-2422-400000i2−i2−2i22i2i2i2−i2−i2−2i22i20−2222−2i2i4i−4i-220000i2−i2−2i22i2i2i2−i2−i20000000000−2i2i2−2−222222−2−2000000000000000000000000000000000
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χ1068-8-4-4-404444i2−4i200222-2-2-200−6i6i0−2i22i2−2i22i2−2ζ+4ζ34ζ−2ζ32ζ−4ζ3−4ζ+2ζ3−2i22i20000000-11003i−3ii2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ300000000000000000000000000000000000000000000000000000
χ1078-8-4-4-40444−4i24i200222-2-2-2006i−6i02i2−2i22i2−2i2−4ζ+2ζ32ζ−4ζ34ζ−2ζ3−2ζ+4ζ32i2−2i20000000-1100−3i3i−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ300000000000000000000000000000000000000000000000000000
χ1088-8-4-4-40444−4i24i200222-2-2-200−6i6i02i2−2i22i2−2i22ζ−4ζ3−4ζ+2ζ3−2ζ+4ζ34ζ−2ζ32i2−2i20000000-11003i−3i−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ300000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.