Finite Group Databasebeta

← Group #13178469

Character table — Group #13178469

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222224444444444444444448888888888888888888888816161616161616161616181818181818181818183636363636363636363636363636367272727272727272
order1233346662233333666668121212242466666612121212122424242424242424242424246666666666222444668822224466881212122424666612122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-1-1-11-11-11-11-1-11-1-1-11-1-1-11-11-1
χ4111111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-11-11-11-11-1-11-1-1-11-1-1-11-11
χ51111111111-11111111111-1111-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111111111-1-11-11-1-1111-1-1111-1-11-11-1-11-1-1
χ61111111111-11111111111-1111-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-11-1-11-1-111-1-11-1-111-1-1-1111-1-1-1-1-111-11-111
χ71111111111-11111111111-1111-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-11-1-1-111-1111-1-11-1-11-11-11111-11-1-1-11
χ81111111111-11111111111-1111-1-111-1-11-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-11-1-111-11-1-111-111-1-1-1111-1-1-11111-1
χ9111111111-111111111111-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11-111-111-1-1111-1-1-11-111-1-1-1
χ10111111111-111111111111-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-111-1-1-111-1-11-1-1111-1-1-1-11-1-11-1111
χ11111111111-111111111111-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-1111-1-1-1111-1-11-11-111-1-11-111-11
χ12111111111-111111111111-1111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-11-1-1111-111-1-1-111-1-1-1111111-1-1-11-1
χ13111111111-1-11111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111111-1-1-1-1-1-111
χ14111111111-1-11111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-11-1-11111-1-111-1-1
χ15111111111-1-11111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111-11-111-11-1-11-1-1-1-1111-111-1
χ16111111111-1-11111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111-11-1-11-11-1-11-1-11-1111-1-11
χ1722222-22220022222222220-2-2-200000000-2-2-2-2-2000000000000000000000022-2-2-2222000000002-200-2-220000000000
χ1822222-22220022222222220-2-2-200000000-2-2-2-2-200000000000000000000002-22-22-22200000000-2200-22-20000000000
χ1922222-22220022222222220-2-2-200000000-2-2-2-2-20000000000000000000000-2222-2-2-2-20000000022002-2-20000000000
χ2022222-22220022222222220-2-2-200000000-2-2-2-2-20000000000000000000000-2-2-2222-2-200000000-2-2002220000000000
χ212222-12-122222-1-1-1-12-1-1-1-12-122-1-12222-1-12-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1200200-1-1222200000000-100-1-100-1-10000
χ222222-12-122222-1-1-1-12-1-1-1-12-122-1-12222-1-12-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-12-1-1-1-1-200-20011-2-2-2-2000000001001100110000
χ232222-12-1222-22-1-1-1-12-1-1-1-1-2-1221122-2-2-112-1-1-1-1-2-2-2-2111111112-1-1-1-1-21111200200-1-1-2-22-200000000-1001100-110000
χ242222-12-1222-22-1-1-1-12-1-1-1-1-2-1221122-2-2-112-1-1-1-1-2-2-2-2111111112-1-1-1-1-21111-200-2001122-2200000000100-1-1001-10000
χ252222-12-122-222-1-1-1-12-1-1-1-1-2-12211-2-2221-12-1-1-1-1-2-2-2-211111111-211112-1-1-1-1200200-1-1-2-2-2200000000-10011001-10000
χ262222-12-122-222-1-1-1-12-1-1-1-1-2-12211-2-2221-12-1-1-1-1-2-2-2-211111111-211112-1-1-1-1-200-20011222-200000000100-1-100-110000
χ272222-12-122-2-22-1-1-1-12-1-1-1-12-122-1-1-2-2-2-2112-1-1-1-12222-1-1-1-1-1-1-1-1-21111-21111200200-1-122-2-200000000-100-1-100110000
χ282222-12-122-2-22-1-1-1-12-1-1-1-12-122-1-1-2-2-2-2112-1-1-1-12222-1-1-1-1-1-1-1-1-21111-21111-200-20011-2-222000000001001100-1-10000
χ29222-12222-122-12-1-1-1-12-1-1-1222-1222-12-122-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-100200200000002020-10200-1000-1000-10-1
χ30222-12222-122-12-1-1-1-12-1-1-1222-1222-12-122-12-1-1-12-1-1-122-1-1-1-1-1-1-12-1-1-1-12-1-1-100-200-20000000-20-2010-20010001000101
χ31222-12222-12-2-12-1-1-1-12-1-1-1-222-1-2-22-1-212-2-12-1-1-1-2111-2-2111111-12-1-1-11-21110020020000000-2020-10-200-10001000-101
χ32222-12222-12-2-12-1-1-1-12-1-1-1-222-1-2-22-1-212-2-12-1-1-1-2111-2-2111111-12-1-1-11-211100-200-2000000020-20102001000-100010-1
χ33222-12222-1-22-12-1-1-1-12-1-1-1-222-1-2-2-212-1-22-12-1-1-1-2111-2-21111111-2111-12-1-1-1002002000000020-20-10-200-1000-1000101
χ34222-12222-1-22-12-1-1-1-12-1-1-1-222-1-2-2-212-1-22-12-1-1-1-2111-2-21111111-2111-12-1-1-100-200-20000000-20201020010001000-10-1
χ35222-12222-1-2-2-12-1-1-1-12-1-1-1222-122-21-21-2-2-12-1-1-12-1-1-122-1-1-1-1-1-11-21111-21110020020000000-20-20-10200-1000100010-1
χ36222-12222-1-2-2-12-1-1-1-12-1-1-1222-122-21-21-2-2-12-1-1-12-1-1-122-1-1-1-1-1-11-21111-211100-200-20000000202010-2001000-1000-101
χ3722-12222-1222-1-12-1-1-1-12-1-122-1222-12-1222-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-10200200000002020-10200-1000-1000-10-10
χ3822-12222-1222-1-12-1-1-1-12-1-122-1222-12-1222-1-12-1-1-12-1-1-1-122-1-1-1-1-1-12-1-1-1-12-1-10-200-20000000-20-2010-200100010001010
χ3922-12222-122-2-1-12-1-1-1-12-1-1-22-12-2-2-121-22-2-1-12-1-11-21111-2-21111-1-12-1-111-21102002000000020-20-10-200-1000-10001010
χ4022-12222-122-2-1-12-1-1-1-12-1-1-22-12-2-2-121-22-2-1-12-1-11-21111-2-21111-1-12-1-111-2110-200-20000000-20201020010001000-10-10
χ4122-12222-12-22-1-12-1-1-1-12-1-1-22-12-2-21-2-12-22-1-12-1-11-21111-2-2111111-211-1-12-1-1020020000000-2020-10-200-10001000-1010
χ4222-12222-12-22-1-12-1-1-1-12-1-1-22-12-2-21-2-12-22-1-12-1-11-21111-2-2111111-211-1-12-1-10-200-2000000020-20102001000-100010-10
χ4322-12222-12-2-2-1-12-1-1-1-12-1-122-12221-21-2-2-2-1-12-1-1-12-1-1-1-122-1-1-1-111-21111-211020020000000-20-20-10200-1000100010-10
χ4422-12222-12-2-2-1-12-1-1-1-12-1-122-12221-21-2-2-2-1-12-1-1-12-1-1-1-122-1-1-1-111-21111-2110-200-20000000202010-2001000-1000-1010
χ454444-2-4-244004-2-2-2-24-2-2-2-202-4-400000000-422220000000000000000000000400-400-2-20000000000002000000000000
χ464444-2-4-244004-2-2-2-24-2-2-2-202-4-400000000-422220000000000000000000000-40040022000000000000-2000000000000
χ47444-24-444-200-24-2-2-2-24-2-2-20-4-42000000002-4222000000000000000000000000400-400000000000-2000020000000000
χ48444-24-444-200-24-2-2-2-24-2-2-20-4-42000000002-4222000000000000000000000000-40040000000000020000-20000000000
χ49444-2-24-24-244-2-2111-2-21114-24-2-2-24-24-2-2-2-2-21114-2-2-2-2-2111111-2-2111-2-2111000000000000000000000000000000000
χ50444-2-24-24-24-4-2-2111-2-2111-4-24-2224-2-42-22-2-2111-422222-1-1-1-1-1-1-2-211122-1-1-1000000000000000000000000000000000
χ51444-2-24-24-2-44-2-2111-2-2111-4-24-222-424-22-2-2-2111-422222-1-1-1-1-1-122-1-1-1-2-2111000000000000000000000000000000000
χ52444-2-24-24-2-4-4-2-2111-2-21114-24-2-2-2-42-4222-2-21114-2-2-2-2-211111122-1-1-122-1-1-1000000000000000000000000000000000
χ5344-244-44-2400-2-24-2-2-2-24-2-20-42-40000000022-42200000000000000000000000400-400000000000-20000200000000000
χ5444-244-44-2400-2-24-2-2-2-24-2-20-42-40000000022-42200000000000000000000000-40040000000000020000-200000000000
χ5544-24-24-2-2444-21-211-21-2114-2-24-2-2-24-24-2-2-21-211-24-2-211-2-21111-21-211-21-211000000000000000000000000000000000
χ5644-24-24-2-244-4-21-211-21-211-4-2-2422-242-4-22-21-2112-422-1-122-1-1-1-1-21-2112-12-1-1000000000000000000000000000000000
χ5744-24-24-2-24-44-21-211-21-211-4-2-24222-4-242-2-21-2112-422-1-122-1-1-1-12-12-1-1-21-211000000000000000000000000000000000
χ5844-24-24-2-24-4-4-21-211-21-2114-2-24-2-22-42-422-21-211-24-2-211-2-211112-12-1-12-12-1-1000000000000000000000000000000000
χ5944-2-2444-2-2441-2-2111-2-21144-2-244-2-2-2-2441-2-211-2-211-2-2-2-211111-2-2111-2-211000000000000000000000000000000000
χ6044-2-2444-2-24-41-2-2111-2-211-44-2-2-4-4-2-2224-41-2-21122-1-12222-1-1-1-11-2-211-122-1-1000000000000000000000000000000000
χ6144-2-2444-2-2-441-2-2111-2-211-44-2-2-4-422-2-2-441-2-21122-1-12222-1-1-1-1-122-1-11-2-211000000000000000000000000000000000
χ6244-2-2444-2-2-4-41-2-2111-2-21144-2-2442222-4-41-2-211-2-211-2-2-2-21111-122-1-1-122-1-1000000000000000000000000000000000
χ6344-2-2-24-2-2-244111−1−3i32−1+3i32111−1−3i32−1+3i324-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32000000000000000000000000000000000
χ6444-2-2-24-2-2-244111−1+3i32−1−3i32111−1+3i32−1−3i324-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32000000000000000000000000000000000
χ6544-2-2-24-2-2-24-4111−1−3i32−1+3i32111−1−3i32−1+3i32-4-2-2-222-2-222-22111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32-1-1-11+3i321−3i32000000000000000000000000000000000
χ6644-2-2-24-2-2-24-4111−1+3i32−1−3i32111−1+3i32−1−3i32-4-2-2-222-2-222-22111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32-1-1-11−3i321+3i32000000000000000000000000000000000
χ6744-2-2-24-2-2-2-44111−1−3i32−1+3i32111−1−3i32−1+3i32-4-2-2-22222-2-22-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32-1-1-11+3i321−3i32111−1−3i32−1+3i32000000000000000000000000000000000
χ6844-2-2-24-2-2-2-44111−1+3i32−1−3i32111−1+3i32−1−3i32-4-2-2-22222-2-22-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-1-1-11−3i321+3i32111−1+3i32−1−3i32000000000000000000000000000000000
χ6944-2-2-24-2-2-2-4-4111−1−3i32−1+3i32111−1−3i32−1+3i324-2-2-2-2-2222222111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-11+3i321−3i32-1-1-11+3i321−3i32000000000000000000000000000000000
χ7044-2-2-24-2-2-2-4-4111−1+3i32−1−3i32111−1+3i32−1−3i324-2-2-2-2-2222222111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-11−3i321+3i32-1-1-11−3i321+3i32000000000000000000000000000000000
χ714-44440-4-4-40044444-4-4-4-4-40000000000000000000000000000000000000000000000022−22000000000000022−2200000000
χ724-44440-4-4-40044444-4-4-4-4-400000000000000000000000000000000000000000000000−22220000000000000−222200000000
χ734-444-202-4-4004-2-2-2-2-422220000i6−i6000000000000000i6−i6i6−i6i6−i6i6−i60000000000000000−2i32i322−220000000000000−2200000000
χ744-444-202-4-4004-2-2-2-2-422220000i6−i6000000000000000i6−i6i6−i6i6−i6i6−i600000000000000002i3−2i3−222200000000000002−200000000
χ754-444-202-4-4004-2-2-2-2-422220000−i6i6000000000000000−i6i6−i6i6−i6i6−i6i60000000000000000−2i32i3−222200000000000002−200000000
χ764-444-202-4-4004-2-2-2-2-422220000−i6i6000000000000000−i6i6−i6i6−i6i6−i6i600000000000000002i3−2i322−220000000000000−2200000000
χ77888-4-4-8-48-400-4-4222-4-422204-840000000044-2-2-20000000000000000000000000000000000000000000000000000000
χ7888-48-4-8-4-4800-42-422-42-422044-8000000004-24-2-20000000000000000000000000000000000000000000000000000000
χ7988-4-48-88-4-4002-4-4222-4-4220-84400000000-244-2-20000000000000000000000000000000000000000000000000000000
χ8088-4-4-4-8-4-4-400222−1−3i3−1+3i3222−1−3i3−1+3i3044400000000-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000
χ8188-4-4-4-8-4-4-400222−1+3i3−1−3i3222−1+3i3−1−3i3044400000000-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000
χ828-88-480-8-8400-48-4-4-44-8444000000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-4-404-8400-4-422244-2-2-200002i6−2i60000000000000002i6−2i6−i6i6−i6i6−i6i60000000000000000000000000000000000000000000
χ848-88-4-404-8400-4-422244-2-2-20000−2i62i6000000000000000−2i62i6i6−i6i6−i6i6−i60000000000000000000000000000000000000000000
χ858-8-4880-84-800-4-48-4-444-844000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-48-4044-800-42-4224-24-2-200002i6−2i6000000000000000−i6i62i6−2i6−i6i6−i6i60000000000000000000000000000000000000000000
χ878-8-48-4044-800-42-4224-24-2-20000−2i62i6000000000000000i6−i6−2i62i6i6−i6i6−i60000000000000000000000000000000000000000000
χ888-8-4-480-844002-4-422-244-2-2000000000000000000032−32000032−32−32320000000000000000000000000000000000000000000
χ898-8-4-480-844002-4-422-244-2-20000000000000000000−32320000−323232−320000000000000000000000000000000000000000000
χ908-8-4-4-4044400222−1−3i3−1+3i3-2-2-21+3i31−3i300002i6−2i60000000000000−3232−i6i6−i6i6−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ232ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ230000000000000000000000000000000000000000000
χ918-8-4-4-4044400222−1−3i3−1+3i3-2-2-21+3i31−3i30000−2i62i6000000000000032−32i6−i6i6−i6ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ23−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ230000000000000000000000000000000000000000000
χ928-8-4-4-4044400222−1+3i3−1−3i3-2-2-21−3i31+3i300002i6−2i6000000000000032−32−i6i6−i6i62ζ5−ζ7+ζ13−2ζ23−2ζ5+ζ7−ζ13+2ζ23−ζ5+2ζ7−2ζ13+ζ23ζ5−2ζ7+2ζ13−ζ230000000000000000000000000000000000000000000
χ938-8-4-4-4044400222−1+3i3−1−3i3-2-2-21−3i31+3i30000−2i62i60000000000000−3232i6−i6i6−i6−2ζ5+ζ7−ζ13+2ζ232ζ5−ζ7+ζ13−2ζ23ζ5−2ζ7+2ζ13−ζ23−ζ5+2ζ7−2ζ13+ζ230000000000000000000000000000000000000000000

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