Finite Group Databasebeta

← Group #13178466

Character table — Group #13178466

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1122222222244444444444444444444488888888888888888888899999916161616161616161616181818181818181818181818181818363636363636363636363636363636727272727272
order123334666882233333666661212122424242424246666661212121212242424242424242424242244446666666666224668888881212121222444466122424242424246612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111-1-111-1-111111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-11-1-1-1-111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-11-1-1-1-1-1-1-111-1-111-1-1-1-111-11-1-1-1-1-111-1-1-1-111
χ511111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ611111111111-1-11111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-11111
χ711111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-111-1-1111-1-1-1-111-1-111-1-111
χ811111111111-1-11111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1111111-1-1-11-1-1-1-1-1111111-1-1
χ9111111111-1-11-11111111111111-1-1-1-1-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111111-1-1-1-1-1-111111-11-11-1111-1-1-1-1-1-11-11-11-1
χ10111111111-1-11-11111111111111-1-1-1-1-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1111-1-11111-1-1-1-11-1-11-11-1-11-1-111111-1-11-11
χ11111111111-1-11-11111111111111-1-1-1-1-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-11-1-1-1-111-1-11111-1-1-111-1-111-1-111-1-111-111-1-11
χ12111111111-1-11-11111111111111-1-1-1-1-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-1-1-111-11-111-1-11-11111-1-1-11-111-1
χ13111111111-1-1-111111111111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111111111-1-1-1-1-1-11111-11-11-11111-1-1-1-1-1-1-11-11-11
χ14111111111-1-1-111111111111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1111-1-11111-1-1-1-1-111-11-1-1-11-1-11111-111-11-1
χ15111111111-1-1-111111111111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-11-1-111-11-1-111-1-1111-1-111-1
χ16111111111-1-1-111111111111111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-11-1-1-11111-1-1-1-1111-11-1-11-11-11111-1-11-11-1-11
χ1722222-222200002222222222-2-2-2000000000000-2-2-2-2-200000000002222220000000000-2-2-2220000002222000000-2-2-2000000000000
χ1822222-222200002222222222-2-2-2000000000000-2-2-2-2-2000000000022-2-2-2-2000000000022-222000000-2-2-2-200000022-2000000000000
χ1922222-222200002222222222-2-2-2000000000000-2-2-2-2-20000000000-2-222-2-20000000000-222-2-200000022-2-2000000-222000000000000
χ2022222-222200002222222222-2-2-2000000000000-2-2-2-2-20000000000-2-2-2-22200000000002-22-2-2000000-2-2220000002-22000000000000
χ212222-12-12222222-1-1-1-12-1-1-1-1-1222222-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-12200002-1-1-1-12-1-1-1-1002-1-1220000000022000000-1-1-10000-1-10000
χ222222-12-12222222-1-1-1-12-1-1-1-1-1222222-1-12222-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-200002-1-1-1-12-1-1-1-100-211-2-200000000-2-20000001110000110000
χ232222-12-12222-2-22-1-1-1-12-1-1-1-1-1222222-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-1220000-21111-21111002-1-12200000000-2-2000000-1-1-10000110000
χ242222-12-12222-2-22-1-1-1-12-1-1-1-1-1222222-1-1-2-2-2-2112-1-1-1-122-1-1-1-1-1-1-1-1-2-20000-21111-2111100-211-2-200000000220000001110000-1-10000
χ252222-12-122-2-22-22-1-1-1-12-1-1-1-1-122-2-2-2-21122-2-2-112-1-1-1-1-2-2111111112200002-1-1-1-1-21111002-1-1-2-2000000002-2000000-1110000-110000
χ262222-12-122-2-22-22-1-1-1-12-1-1-1-1-122-2-2-2-21122-2-2-112-1-1-1-1-2-211111111-2-200002-1-1-1-1-2111100-2112200000000-220000001-1-100001-10000
χ272222-12-122-2-2-222-1-1-1-12-1-1-1-1-122-2-2-2-211-2-2221-12-1-1-1-1-2-211111111220000-211112-1-1-1-1002-1-1-2-200000000-22000000-11100001-10000
χ282222-12-122-2-2-222-1-1-1-12-1-1-1-1-122-2-2-2-211-2-2221-12-1-1-1-1-2-211111111-2-20000-211112-1-1-1-100-21122000000002-20000001-1-10000-110000
χ29222-12222-12222-12-1-1-1-12-1-1-122-122-1-1222-12-122-12-1-1-1-1-122-1-1-1-1-1-1000022-12-1-1-1-12-1-1-10200000002200-1-10000220-100000-1-10000-1-1
χ30222-12222-12222-12-1-1-1-12-1-1-122-122-1-1222-12-122-12-1-1-1-1-122-1-1-1-1-1-10000-2-2-12-1-1-1-12-1-1-10-20000000-2-200110000-2-2010000011000011
χ31222-12222-122-2-2-12-1-1-1-12-1-1-122-122-1-122-21-21-2-2-12-1-1-1-1-122-1-1-1-1-1-10000221-21111-21110200000002200-1-10000-2-20-100000-1-1000011
χ32222-12222-122-2-2-12-1-1-1-12-1-1-122-122-1-122-21-21-2-2-12-1-1-1-1-122-1-1-1-1-1-10000-2-21-21111-21110-20000000-2-200110000220100000110000-1-1
χ33222-12222-1-2-22-2-12-1-1-1-12-1-1-122-1-2-211-2-22-1-212-2-12-1-1-111-2-2111111000022-12-1-1-11-2111020000000-2-200-1-100002-20-100000110000-11
χ34222-12222-1-2-22-2-12-1-1-1-12-1-1-122-1-2-211-2-22-1-212-2-12-1-1-111-2-21111110000-2-2-12-1-1-11-21110-200000002200110000-220100000-1-100001-1
χ35222-12222-1-2-2-22-12-1-1-1-12-1-1-122-1-2-211-2-2-212-1-22-12-1-1-111-2-21111110000221-2111-12-1-1-1020000000-2-200-1-10000-220-1000001100001-1
χ36222-12222-1-2-2-22-12-1-1-1-12-1-1-122-1-2-211-2-2-212-1-22-12-1-1-111-2-21111110000-2-21-2111-12-1-1-10-2000000022001100002-20100000-1-10000-11
χ3722-12222-122222-1-12-1-1-1-12-1-12-12-1-12222-12-1222-1-12-1-1-1-1-1-122-1-1-1-1002200-1-12-1-1-1-12-1-120000002200-1-100002200-10000-1-10000-1-100
χ3822-12222-122222-1-12-1-1-1-12-1-12-12-1-12222-12-1222-1-12-1-1-1-1-1-122-1-1-1-100-2-200-1-12-1-1-1-12-1-1-2000000-2-200110000-2-200100001100001100
χ3922-12222-1222-2-2-1-12-1-1-1-12-1-12-12-1-122221-21-2-2-2-1-12-1-1-1-1-1-122-1-1-1-100220011-21111-21120000002200-1-10000-2-200-10000-1-100001100
χ4022-12222-1222-2-2-1-12-1-1-1-12-1-12-12-1-122221-21-2-2-2-1-12-1-1-1-1-1-122-1-1-1-100-2-20011-21111-211-2000000-2-200110000220010000110000-1-100
χ4122-12222-12-2-22-2-1-12-1-1-1-12-1-12-1211-2-2-2-2-121-22-2-1-12-1-11111-2-21111002200-1-12-1-111-2112000000-2-200-1-100002-200-10000110000-1100
χ4222-12222-12-2-22-2-1-12-1-1-1-12-1-12-1211-2-2-2-2-121-22-2-1-12-1-11111-2-2111100-2-200-1-12-1-111-211-20000002200110000-220010000-1-100001-100
χ4322-12222-12-2-2-22-1-12-1-1-1-12-1-12-1211-2-2-2-21-2-12-22-1-12-1-11111-2-2111100220011-211-1-12-1-12000000-2-200-1-10000-2200-100001100001-100
χ4422-12222-12-2-2-22-1-12-1-1-1-12-1-12-1211-2-2-2-21-2-12-22-1-12-1-11111-2-2111100-2-20011-211-1-12-1-1-200000022001100002-20010000-1-10000-1100
χ452-22220-2-2-22−20022222-2-2-2-2-20002−22−22−2000000000002−22−22−222−2−22-22i−2i2i−2i00000000000002-22−2−i2i2−i2i22i−2i2i−2i0000000002−2−i2i2−i2i2000000
χ462-22220-2-2-22−20022222-2-2-2-2-20002−22−22−2000000000002−22−22−222−2−22-2−2i2i−2i2i00000000000002-22−2i2−i2i2−i2−2i2i−2i2i0000000002−2i2−i2i2−i2000000
χ472-22220-2-2-22−20022222-2-2-2-2-20002−22−22−2000000000002−22−22−222−2−2-222i−2i−2i2i0000000000000-22−22−i2i2i2−i22i−2i−2i2i000000000−22−i2i2i2−i2000000
χ482-22220-2-2-22−20022222-2-2-2-2-20002−22−22−2000000000002−22−22−222−2−2-22−2i2i2i−2i0000000000000-22−22i2−i2−i2i2−2i2i2i−2i000000000−22i2−i2−i2i2000000
χ492-22220-2-2-2−220022222-2-2-2-2-2000−22−22−2200000000000−22−22−22−2−2222-22i−2i2i−2i00000000000002-2−22i2−i2i2−i22i−2i2i−2i000000000−22i2−i2i2−i2000000
χ502-22220-2-2-2−220022222-2-2-2-2-2000−22−22−2200000000000−22−22−22−2−2222-2−2i2i−2i2i00000000000002-2−22−i2i2−i2i2−2i2i−2i2i000000000−22−i2i2−i2i2000000
χ512-22220-2-2-2−220022222-2-2-2-2-2000−22−22−2200000000000−22−22−22−2−222-222i−2i−2i2i0000000000000-222−2i2−i2−i2i22i−2i−2i2i0000000002−2i2−i2−i2i2000000
χ522-22220-2-2-2−220022222-2-2-2-2-2000−22−22−2200000000000−22−22−22−2−222-22−2i2i2i−2i0000000000000-222−2−i2i2i2−i2−2i2i2i−2i0000000002−2−i2i2i2−i2000000
χ534444-2-4-24400004-2-2-2-24-2-2-2-22-4-4000000000000-422220000000000440000000000000000-4-2-20000000000000000002000000000000
χ544444-2-4-24400004-2-2-2-24-2-2-2-22-4-4000000000000-422220000000000-4-40000000000000000422000000000000000000-2000000000000
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χ57444-2-24-24-24444-2-2111-2-2111-24-244-2-2-2-24-24-2-2-2-2-2111-2-2-2-2111111000000-2-2111-2-2111000000000000000000000000000000000000
χ58444-2-24-24-244-4-4-2-2111-2-2111-24-244-2-2-2-2-42-4222-2-2111-2-2-2-211111100000022-1-1-122-1-1-1000000000000000000000000000000000000
χ59444-2-24-24-2-4-44-4-2-2111-2-2111-24-2-4-422224-2-42-22-2-21112222-1-1-1-1-1-1000000-2-211122-1-1-1000000000000000000000000000000000000
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χ6544-24-24-2-24-4-44-4-21-211-21-211-2-2422-4-422-242-4-22-21-21122-1-122-1-1-1-1000000-21-2112-12-1-1000000000000000000000000000000000000
χ6644-24-24-2-24-4-4-44-21-211-21-211-2-2422-4-4222-4-242-2-21-21122-1-122-1-1-1-10000002-12-1-1-21-211000000000000000000000000000000000000
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χ6944-2-2444-2-2-4-44-41-2-2111-2-2114-2-22222-4-4-2-2224-41-2-211-1-12222-1-1-1-10000001-2-211-122-1-1000000000000000000000000000000000000
χ7044-2-2444-2-2-4-4-441-2-2111-2-2114-2-22222-4-422-2-2-441-2-211-1-12222-1-1-1-1000000-122-1-11-2-211000000000000000000000000000000000000
χ7144-2-2-24-2-2-24444111−1−3i32−1+3i32111−1−3i32−1+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+3i32000000111−1−3i32−1+3i32111−1−3i32−1+3i32000000000000000000000000000000000000
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χ7644-2-2-24-2-2-2-4-44-4111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2222222-2-222-22111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000111−1+3i32−1−3i32-1-1-11−3i321+3i32000000000000000000000000000000000000
χ7744-2-2-24-2-2-2-4-4-44111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-222222222-2-22-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000000000000000
χ7844-2-2-24-2-2-2-4-4-44111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-222222222-2-22-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000000000000000
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χ804-444-202-4-422−22004-2-2-2-2-4222200022−2222−22−220000000000022−22−22−22−2−222-44000000000000000002-2−2222000000000000000002−20000000000
χ814-444-202-4-4−2222004-2-2-2-2-42222000−2222−22222−200000000000−22222−22−222−2−24-400000000000000000-22−2222000000000000000002−20000000000
χ824-444-202-4-4−2222004-2-2-2-2-42222000−2222−22222−200000000000−22222−22−222−2−2-44000000000000000002-222−2200000000000000000−220000000000
χ834-44-240-4-4222−2200-24-2-2-22-422200022−22−2222−2200000000000−2222−22−22−2−22200004i−4i0000000000000000000−2i22i200−2i2i0000000000000i2−i2000000
χ844-44-240-4-4222−2200-24-2-2-22-422200022−22−2222−2200000000000−2222−22−22−2−2220000−4i4i00000000000000000002i2−2i2002i−2i0000000000000−i2i2000000
χ854-44-240-4-42−222200-24-2-2-22-4222000−22222−2−2222000000000002−2−22222−222−2−200004i−4i00000000000000000002i2−2i200−2i2i0000000000000−i2i2000000
χ864-44-240-4-42−222200-24-2-2-22-4222000−22222−2−2222000000000002−2−22222−222−2−20000−4i4i0000000000000000000−2i22i2002i−2i0000000000000i2−i2000000
χ874-4-2440-42-422−2200-2-24-2-222-422000−2222−2222−2200000000000−22−2222−22−2−222004i−4i0000000000000000000−2i22i200−2i2i0000000000000i2−i200000000
χ884-4-2440-42-422−2200-2-24-2-222-422000−2222−2222−2200000000000−22−2222−22−2−22200−4i4i00000000000000000002i2−2i2002i−2i0000000000000−i2i200000000
χ894-4-2440-42-4−222200-2-24-2-222-4220002−2−2222−2222000000000002−22−2−222222−2−2004i−4i00000000000000000002i2−2i200−2i2i0000000000000−i2i200000000
χ904-4-2440-42-4−222200-2-24-2-222-4220002−2−2222−2222000000000002−22−2−222222−2−200−4i4i0000000000000000000−2i22i2002i−2i0000000000000i2−i200000000
χ91888-4-4-8-48-40000-4-4222-4-42224-8400000000000044-2-2-200000000000000000000000000000000000000000000000000000000000000
χ9288-48-4-8-4-480000-42-422-42-42244-80000000000004-24-2-200000000000000000000000000000000000000000000000000000000000000
χ9388-4-48-88-4-400002-4-4222-4-422-844000000000000-244-2-200000000000000000000000000000000000000000000000000000000000000
χ9488-4-4-4-8-4-4-40000222−1−3i3−1+3i3222−1−3i3−1+3i3444000000000000-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000
χ9588-4-4-4-8-4-4-40000222−1+3i3−1−3i3222−1+3i3−1−3i3444000000000000-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000
χ968-88-4-404-8442−4200-4-422244-2-2-200042−42−2222−222200000000000−2222−22222−222−2−20000000000000000000000000000000000000000000000000000
χ978-88-4-404-84−424200-4-422244-2-2-2000−424222−2222−220000000000022−2222−22−22−2−2220000000000000000000000000000000000000000000000000000
χ988-8-48-4044-842−4200-42-4224-24-2-2000−222242−42−222200000000000−22222−2−222222−2−20000000000000000000000000000000000000000000000000000
χ998-8-48-4044-8−424200-42-4224-24-2-200022−22−424222−220000000000022−22−2222−22−2−2220000000000000000000000000000000000000000000000000000
χ1008-8-4-480-84442−42002-4-422-244-2-2000−2222−222242−42000000000002−2−2222−222222−2−20000000000000000000000000000000000000000000000000000
χ1018-8-4-480-844−4242002-4-422-244-2-200022−2222−22−424200000000000−2222−2222−22−2−2220000000000000000000000000000000000000000000000000000
χ1028-8-4-4-4044442−4200222−1−3i3−1+3i3-2-2-21+3i31−3i3000−2222−2222−2222000000000002−22−22−2−ζ5−2ζ7+2ζ13+ζ232ζ5+ζ7−ζ13−2ζ23ζ5+2ζ7−2ζ13−ζ23−2ζ5−ζ7+ζ13+2ζ230000000000000000000000000000000000000000000000000000
χ1038-8-4-4-4044442−4200222−1+3i3−1−3i3-2-2-21−3i31+3i3000−2222−2222−2222000000000002−22−22−22ζ5+ζ7−ζ13−2ζ23−ζ5−2ζ7+2ζ13+ζ23−2ζ5−ζ7+ζ13+2ζ23ζ5+2ζ7−2ζ13−ζ230000000000000000000000000000000000000000000000000000
χ1048-8-4-4-40444−424200222−1−3i3−1+3i3-2-2-21+3i31−3i300022−2222−2222−2200000000000−22−22−22ζ5+2ζ7−2ζ13−ζ23−2ζ5−ζ7+ζ13+2ζ23−ζ5−2ζ7+2ζ13+ζ232ζ5+ζ7−ζ13−2ζ230000000000000000000000000000000000000000000000000000
χ1058-8-4-4-40444−424200222−1+3i3−1−3i3-2-2-21−3i31+3i300022−2222−2222−2200000000000−22−22−22−2ζ5−ζ7+ζ13+2ζ23ζ5+2ζ7−2ζ13−ζ232ζ5+ζ7−ζ13−2ζ23−ζ5−2ζ7+2ζ13+ζ230000000000000000000000000000000000000000000000000000

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