Finite Group Databasebeta

← Group #13178475

Character table — Group #13178475

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1122222222244444444444444444444488888888888888888888899999916161616161616161616181818181818181818181818181818363636363636363636363636363636727272727272
order1233346668823333346666612121224242424242466612121212121212122424242424242424242422444466666121212121222466888888121212122224446612242424242424666121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111-1-1-1-11-1-11-1-1
χ311111111111111111111111111111111111111111111111111111-1-111-1-111111111111-1-1-1-1-1-111-1-111-1-1-11-1-11-11-1-1-1-111-1-1-11-1-11-1
χ411111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-11-1-1-1-1-1-1-111-1-111-1-11-1-11-11-1-1-1-1-111-1-11-1-11
χ511111111111-111111-111111111111111-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ611111111111-111111-111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-1-111-111
χ711111111111-111111-111111111111111-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-111-1-11-111-111-1-1-1-111-1-11-111-11
χ811111111111-111111-111111111111111-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-11111-111-1-11-1-1-1-1-11111-111-1
χ9111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-111111-1-1-1-1-1-111111-1-1-111111-1-1-1-1-1-11-1-1-111
χ10111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1111-1-11111-1-1-1-1111-1-1-1-1-11-1-11111111-1-1-1
χ11111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-1111-11-1-111-1-111-1-1111-1
χ12111111111-1-1111111-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-1-1-111-11-11-11-11-11111-1-1-11-11-11
χ13111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111111111-1-1-1-1-1-11111-1111-1-1111-1-1-1-1-1-1-1111-1-1
χ14111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-1111-1-11111-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1111
χ15111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-111-1-111-1-11111-1-1-11
χ16111111111-1-1-111111111111111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-11-1-1-11111-1-1-1-1111-11-11-1-11-11111-1-11-11-11-1
χ1722222-222200022222022222-2-2-2000000000000-2-2-2-2-200000000002222220000000000-2-2-2220000002222000000-2-2-2000000000000
χ1822222-222200022222022222-2-2-2000000000000-2-2-2-2-2000000000022-2-2-2-2000000000022-222000000-2-2-2-200000022-2000000000000
χ1922222-222200022222022222-2-2-2000000000000-2-2-2-2-20000000000-2-222-2-20000000000-222-2-200000022-2-2000000-222000000000000
χ2022222-222200022222022222-2-2-2000000000000-2-2-2-2-20000000000-2-2-2-22200000000002-22-2-2000000-2-2220000002-22000000000000
χ212222-1222-12222-1-1-1-122-1-1-1-122-12222-1-122-122-12-1-1-1-122-1-1-1-1-1-1-1-10000222-1-1-1-12-1-1-1-10200000002200-1-10020020-100000-1-100-100-1
χ222222-1222-12222-1-1-1-122-1-1-1-122-12222-1-122-122-12-1-1-1-122-1-1-1-1-1-1-1-10000-2-22-1-1-1-12-1-1-1-10-20000000-2-2001100-200-2010000011001001
χ232222-1222-122-22-1-1-1-1-22-1-1-1-122-12222-1-1-2-21-2-212-1-1-1-122-1-1-1-1-1-1-1-1000022-21111-211110200000002200-1-100-200-20-100000-1-1001001
χ242222-1222-122-22-1-1-1-1-22-1-1-1-122-12222-1-1-2-21-2-212-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-21111-211110-20000000-2-2001100200201000001100-100-1
χ252222-1222-1-2-222-1-1-1-1-22-1-1-1-122-1-2-2-2-21122-1-2-212-1-1-1-1-2-2111111110000222-1-1-1-1-21111020000000-2-200-1-100-20020-1000001100100-1
χ262222-1222-1-2-222-1-1-1-1-22-1-1-1-122-1-2-2-2-21122-1-2-212-1-1-1-1-2-2111111110000-2-22-1-1-1-1-211110-2000000022001100200-20100000-1-100-1001
χ272222-1222-1-2-2-22-1-1-1-122-1-1-1-122-1-2-2-2-211-2-2122-12-1-1-1-1-2-211111111000022-211112-1-1-1-1020000000-2-200-1-100200-20-1000001100-1001
χ282222-1222-1-2-2-22-1-1-1-122-1-1-1-122-1-2-2-2-211-2-2122-12-1-1-1-1-2-2111111110000-2-2-211112-1-1-1-10-2000000022001100-20020100000-1-100100-1
χ29222-1222-12222-12-1-1-12-12-1-1-12-1222-1-1222-122-12-12-1-1-1-1-122-1-1-1-1-1-1002200-12-1-1-1-12-1-1-120000002200-1-100020020-10000-1-1000-100-10
χ30222-1222-12222-12-1-1-12-12-1-1-12-1222-1-1222-122-12-12-1-1-1-1-122-1-1-1-1-1-100-2-200-12-1-1-1-12-1-1-1-2000000-2-20011000-200-20100001100010010
χ31222-1222-1222-2-12-1-1-1-2-12-1-1-12-1222-1-122-21-2-21-2-12-1-1-1-1-122-1-1-1-1-1-10022001-21111-211120000002200-1-1000-200-20-10000-1-100010010
χ32222-1222-1222-2-12-1-1-1-2-12-1-1-12-1222-1-122-21-2-21-2-12-1-1-1-1-122-1-1-1-1-1-100-2-2001-21111-2111-2000000-2-20011000200201000011000-100-10
χ33222-1222-12-2-22-12-1-1-1-2-12-1-1-12-12-2-211-2-22-12-21-2-12-1-1-111-2-2111111002200-12-1-1-11-21112000000-2-200-1-1000-20020-1000011000100-10
χ34222-1222-12-2-22-12-1-1-1-2-12-1-1-12-12-2-211-2-22-12-21-2-12-1-1-111-2-211111100-2-200-12-1-1-11-2111-2000000220011000200-2010000-1-1000-10010
χ35222-1222-12-2-2-2-12-1-1-12-12-1-1-12-12-2-211-2-2-21-22-12-12-1-1-111-2-21111110022001-2111-12-1-1-12000000-2-200-1-1000200-20-1000011000-10010
χ36222-1222-12-2-2-2-12-1-1-12-12-1-1-12-12-2-211-2-2-21-22-12-12-1-1-111-2-211111100-2-2001-2111-12-1-1-1-2000000220011000-2002010000-1-1000100-10
χ3722-1222-122222-1-12-1-12-1-12-1-1-122-1-12222-122-122-1-12-1-1-1-1-1-122-1-1-1-1220000-1-12-1-1-1-12-1-1002-1-1220000000020020000-1-1-10000-100-100
χ3822-1222-122222-1-12-1-12-1-12-1-1-122-1-12222-122-122-1-12-1-1-1-1-1-122-1-1-1-1-2-20000-1-12-1-1-1-12-1-100-211-2-200000000-200-200001110000100100
χ3922-1222-12222-2-1-12-1-1-2-1-12-1-1-122-1-122221-2-21-2-2-1-12-1-1-1-1-1-122-1-1-1-122000011-21111-211002-1-12200000000-200-20000-1-1-10000100100
χ4022-1222-12222-2-1-12-1-1-2-1-12-1-1-122-1-122221-2-21-2-2-1-12-1-1-1-1-1-122-1-1-1-1-2-2000011-21111-21100-211-2-200000000200200001110000-100-100
χ4122-1222-122-2-22-1-12-1-1-2-1-12-1-1-12211-2-2-2-2-1221-2-2-1-12-1-11111-2-21111220000-1-12-1-111-211002-1-1-2-200000000200-20000-1110000-100100
χ4222-1222-122-2-22-1-12-1-1-2-1-12-1-1-12211-2-2-2-2-1221-2-2-1-12-1-11111-2-21111-2-20000-1-12-1-111-21100-2112200000000-200200001-1-10000100-100
χ4322-1222-122-2-2-2-1-12-1-12-1-12-1-1-12211-2-2-2-21-2-2-122-1-12-1-11111-2-2111122000011-211-1-12-1-1002-1-1-2-200000000-20020000-1110000100-100
χ4422-1222-122-2-2-2-1-12-1-12-1-12-1-1-12211-2-2-2-21-2-2-122-1-12-1-11111-2-21111-2-2000011-211-1-12-1-100-2112200000000200-200001-1-10000-100100
χ452-22220-2-2-2−i2i20222220-2-2-2-2-2000−i2i2−i2i2−i2i200000000000−i2i2−i2i2−i2i2−i2−i2i2i22-22i−2i2i−2i00000000000002-2−i2i22−22−22i−2i2i−2i000000000−i2i22−22−2000000
χ462-22220-2-2-2−i2i20222220-2-2-2-2-2000−i2i2−i2i2−i2i200000000000−i2i2−i2i2−i2i2−i2−i2i2i22-2−2i2i−2i2i00000000000002-2−i2i2−22−22−2i2i−2i2i000000000−i2i2−22−22000000
χ472-22220-2-2-2−i2i20222220-2-2-2-2-2000−i2i2−i2i2−i2i200000000000−i2i2−i2i2−i2i2−i2−i2i2i2-222i−2i−2i2i0000000000000-22i2−i22−2−222i−2i−2i2i000000000i2−i22−2−22000000
χ482-22220-2-2-2−i2i20222220-2-2-2-2-2000−i2i2−i2i2−i2i200000000000−i2i2−i2i2−i2i2−i2−i2i2i2-22−2i2i2i−2i0000000000000-22i2−i2−222−2−2i2i2i−2i000000000i2−i2−222−2000000
χ492-22220-2-2-2i2−i20222220-2-2-2-2-2000i2−i2i2−i2i2−i200000000000i2−i2i2−i2i2−i2i2i2−i2−i22-22i−2i2i−2i00000000000002-2i2−i2−22−222i−2i2i−2i000000000i2−i2−22−22000000
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χ512-22220-2-2-2i2−i20222220-2-2-2-2-2000i2−i2i2−i2i2−i200000000000i2−i2i2−i2i2−i2i2i2−i2−i2-222i−2i−2i2i0000000000000-22−i2i2−222−22i−2i−2i2i000000000−i2i2−222−2000000
χ522-22220-2-2-2i2−i20222220-2-2-2-2-2000i2−i2i2−i2i2−i200000000000i2−i2i2−i2i2−i2i2i2−i2−i2-22−2i2i2i−2i0000000000000-22−i2i22−2−22−2i2i2i−2i000000000−i2i22−2−22000000
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χ7544-2-2-24-2-2-2-4-44111−1−3i32−1+3i32-4111−1−3i32−1+3i32-2-2-2222222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000111−1−3i32−1+3i32-1-1-11+3i321−3i32000000000000000000000000000000000000
χ7644-2-2-24-2-2-2-4-44111−1+3i32−1−3i32-4111−1+3i32−1−3i32-2-2-2222222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000111−1+3i32−1−3i32-1-1-11−3i321+3i32000000000000000000000000000000000000
χ7744-2-2-24-2-2-2-4-4-4111−1−3i32−1+3i324111−1−3i32−1+3i32-2-2-2222222222-2-2-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000000000000000
χ7844-2-2-24-2-2-2-4-4-4111−1+3i32−1−3i324111−1+3i32−1−3i32-2-2-2222222222-2-2-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000000000000000
χ794-444-20-4-42−2i22i204-2-2-2-20-42222000−2i22i2−2i22i2i2−i200000000000−2i22i2i2−i2i2−i2i2i2−i2−i200004i−4i000000000000000000022−2200−2i2i0000000000000−22000000
χ804-444-20-4-42−2i22i204-2-2-2-20-42222000−2i22i2−2i22i2i2−i200000000000−2i22i2i2−i2i2−i2i2i2−i2−i20000−4i4i0000000000000000000−2222002i−2i00000000000002−2000000
χ814-444-20-4-422i2−2i204-2-2-2-20-422220002i2−2i22i2−2i2−i2i2000000000002i2−2i2−i2i2−i2i2−i2−i2i2i200004i−4i0000000000000000000−222200−2i2i00000000000002−2000000
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χ834-44-240-42-4−2i22i20-24-2-2-202-4222000−2i22i2i2−i2−2i22i200000000000i2−i2−2i22i2i2−i2i2i2−i2−i2004i−4i000000000000000000022−2200−2i2i0000000000000−2200000000
χ844-44-240-42-4−2i22i20-24-2-2-202-4222000−2i22i2i2−i2−2i22i200000000000i2−i2−2i22i2i2−i2i2i2−i2−i200−4i4i0000000000000000000−2222002i−2i00000000000002−200000000
χ854-44-240-42-42i2−2i20-24-2-2-202-42220002i2−2i2−i2i22i2−2i200000000000−i2i22i2−2i2−i2i2−i2−i2i2i2004i−4i0000000000000000000−222200−2i2i00000000000002−200000000
χ864-44-240-42-42i2−2i20-24-2-2-202-42220002i2−2i2−i2i22i2−2i200000000000−i2i22i2−2i2−i2i2−i2−i2i2i200−4i4i000000000000000000022−22002i−2i0000000000000−2200000000
χ874-4-24402-4-4−2i22i20-2-24-2-2022-422000i2−i2−2i22i2−2i22i200000000000i2−i2i2−i2−2i22i2i2i2−i2−i24-400000000000000000-22−2i22i200000000000000000i2−i20000000000
χ884-4-24402-4-4−2i22i20-2-24-2-2022-422000i2−i2−2i22i2−2i22i200000000000i2−i2i2−i2−2i22i2i2i2−i2−i2-44000000000000000002-22i2−2i200000000000000000−i2i20000000000
χ894-4-24402-4-42i2−2i20-2-24-2-2022-422000−i2i22i2−2i22i2−2i200000000000−i2i2−i2i22i2−2i2−i2−i2i2i24-400000000000000000-222i2−2i200000000000000000−i2i20000000000
χ904-4-24402-4-42i2−2i20-2-24-2-2022-422000−i2i22i2−2i22i2−2i200000000000−i2i2−i2i22i2−2i2−i2−i2i2i2-44000000000000000002-2−2i22i200000000000000000i2−i20000000000
χ91888-4-4-88-4-4000-4-42220-4-4222-84400000000000044-2-2-200000000000000000000000000000000000000000000000000000000000000
χ9288-48-4-8-48-4000-42-4220-42-4224-840000000000004-24-2-200000000000000000000000000000000000000000000000000000000000000
χ9388-4-48-8-4-480002-4-42202-4-42244-8000000000000-244-2-200000000000000000000000000000000000000000000000000000000000000
χ9488-4-4-4-8-4-4-4000222−1−3i3−1+3i30222−1−3i3−1+3i3444000000000000-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000
χ9588-4-4-4-8-4-4-4000222−1+3i3−1−3i30222−1+3i3−1−3i3444000000000000-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000
χ968-88-4-40-844−4i24i20-4-4222044-2-2-2000−4i24i22i2−2i22i2−2i2000000000002i2−2i22i2−2i2−i2i2−i2−i2i2i20000000000000000000000000000000000000000000000000000
χ978-88-4-40-8444i2−4i20-4-4222044-2-2-20004i2−4i2−2i22i2−2i22i200000000000−2i22i2−2i22i2i2−i2i2i2−i2−i20000000000000000000000000000000000000000000000000000
χ988-8-48-404-84−4i24i20-42-42204-24-2-20002i2−2i2−4i24i22i2−2i2000000000002i2−2i2−i2i22i2−2i2−i2−i2i2i20000000000000000000000000000000000000000000000000000
χ998-8-48-404-844i2−4i20-42-42204-24-2-2000−2i22i24i2−4i2−2i22i200000000000−2i22i2i2−i2−2i22i2i2i2−i2−i20000000000000000000000000000000000000000000000000000
χ1008-8-4-48044-8−4i24i202-4-4220-244-2-20002i2−2i22i2−2i2−4i24i200000000000−i2i22i2−2i22i2−2i2−i2−i2i2i20000000000000000000000000000000000000000000000000000
χ1018-8-4-48044-84i2−4i202-4-4220-244-2-2000−2i22i2−2i22i24i2−4i200000000000i2−i2−2i22i2−2i22i2i2i2−i2−i20000000000000000000000000000000000000000000000000000
χ1028-8-4-4-40444−4i24i20222−1−3i3−1+3i30-2-2-21+3i31−3i30002i2−2i22i2−2i22i2−2i200000000000−i2i2−i2i2−i2i2−ζ5+2ζ7+2ζ13−ζ232ζ5−ζ7−ζ13+2ζ23ζ5−2ζ7−2ζ13+ζ23−2ζ5+ζ7+ζ13−2ζ230000000000000000000000000000000000000000000000000000
χ1038-8-4-4-40444−4i24i20222−1+3i3−1−3i30-2-2-21−3i31+3i30002i2−2i22i2−2i22i2−2i200000000000−i2i2−i2i2−i2i22ζ5−ζ7−ζ13+2ζ23−ζ5+2ζ7+2ζ13−ζ23−2ζ5+ζ7+ζ13−2ζ23ζ5−2ζ7−2ζ13+ζ230000000000000000000000000000000000000000000000000000
χ1048-8-4-4-404444i2−4i20222−1−3i3−1+3i30-2-2-21+3i31−3i3000−2i22i2−2i22i2−2i22i200000000000i2−i2i2−i2i2−i2ζ5−2ζ7−2ζ13+ζ23−2ζ5+ζ7+ζ13−2ζ23−ζ5+2ζ7+2ζ13−ζ232ζ5−ζ7−ζ13+2ζ230000000000000000000000000000000000000000000000000000
χ1058-8-4-4-404444i2−4i20222−1+3i3−1−3i30-2-2-21−3i31+3i3000−2i22i2−2i22i2−2i22i200000000000i2−i2i2−i2i2−i2−2ζ5+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.