Finite Group Databasebeta

← Group #13178467

Character table — Group #13178467

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size11222222244444444444444444488888888888888888888888991616161616161616161618181818181818363636363636363636363636363636367272727272727272
order1233346662233333666668121212242466666612121212122424242424242424242424244466666666662224412122244446668881212242466121212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-11-1-11-1-1-1-111-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111-1-11111111111-11-11-1-1-11-1-1-11-1-11-1-11-11-1-1-11-11-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-11111111111-1-11-11-1-1-11-1-1-11-1-11-1-11-11-1-1-11-11-1-1-11
χ51111111111-11111111111-1111-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-111111111-11-1-11111-1-1-111-1-11-1-111-1-1-1
χ61111111111-11111111111-1111-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-11-1-1-1-111-111-11-11-1-1-111-1-1-1-1-111-11-111
χ71111111111-11111111111-1111-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-11-1-1-111-11-1-1-11-11-111-11111-1-1-11-11
χ81111111111-11111111111-1111-1-11-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-11-1-1-1-1-1111-1-1111-1-1111-1-111-111-1
χ9111111111-111111111111-1111-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111111111-11-111-1111-1-1-111-1-1-111-1-11-1-1
χ10111111111-111111111111-1111-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1111-1-11-111-1-1-111-1-1-1-11-1-11-1111
χ11111111111-111111111111-1111-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-11-1-1-1-1-11-111-11-11-111-111-1-1111-1-11
χ12111111111-111111111111-1111-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-11-1-1111-1-1-1-1-1111-1-111111-1-11-11-1
χ13111111111-1-11111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ14111111111-1-11111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1111-1-11-1-1-1-1111111-1-1-1-1
χ15111111111-1-11111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111-11-11-1-11-11-1-1-1-11-11111-1
χ16111111111-1-11111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-1111-1-1-11-1-11-11-1-11-11-111-11
χ1722222-22220022222222220-2-2-200000000-2-2-2-2-2000000000000220000000000-22-2-2222000000-22-2000-220000000000
χ1822222-22220022222222220-2-2-200000000-2-2-2-2-2000000000000220000000000-2-222-222000000-2-220002-20000000000
χ1922222-22220022222222220-2-2-200000000-2-2-2-2-2000000000000-2-20000000000222-2-2-2-2000000222000-2-20000000000
χ2022222-22220022222222220-2-2-200000000-2-2-2-2-2000000000000-2-200000000002-2-222-2-20000002-2-2000220000000000
χ212222-122-12222-1-1-1-12-1-1-1-122-1222222-12-12-1-1-1-12-122-1-1-1-1-1-1-1-1002-1-1-1-12-1-1-1-1002020002000200-10020-1000-10-1000-1
χ222222-122-12222-1-1-1-12-1-1-1-122-1222222-12-12-1-1-1-12-122-1-1-1-1-1-1-1-1002-1-1-1-12-1-1-1-100-20-2000-2000-200100-2010001010001
χ232222-122-122-22-1-1-1-12-1-1-1-1-22-12-2-22-22-1-212-1-1-1-1-21-2-211111111002-1-1-1-1-2111100202000-2000200-100-20-100010-10001
χ242222-122-122-22-1-1-1-12-1-1-1-1-22-12-2-22-22-1-212-1-1-1-1-21-2-211111111002-1-1-1-1-2111100-20-20002000-200100201000-101000-1
χ252222-122-12-222-1-1-1-12-1-1-1-1-22-12-2-2-22-212-12-1-1-1-1-21-2-21111111100-211112-1-1-1-1002020002000-200-100-20-1000-1010001
χ262222-122-12-222-1-1-1-12-1-1-1-1-22-12-2-2-22-212-12-1-1-1-1-21-2-21111111100-211112-1-1-1-100-20-2000-200020010020100010-1000-1
χ272222-122-12-2-22-1-1-1-12-1-1-1-122-1222-2-2-21-212-1-1-1-12-122-1-1-1-1-1-1-1-100-21111-2111100202000-2000-200-10020-1000101000-1
χ282222-122-12-2-22-1-1-1-12-1-1-1-122-1222-2-2-21-212-1-1-1-12-122-1-1-1-1-1-1-1-100-21111-2111100-20-20002000200100-201000-10-10001
χ29222-122-12222-12-1-1-1-12-1-1-12-1222222-12-12-12-1-1-1-12-1-122-1-1-1-1-1-100-12-1-1-1-12-1-1-102020002000200-10020-1000-10-1000-10
χ30222-122-12222-12-1-1-1-12-1-1-12-1222222-12-12-12-1-1-1-12-1-122-1-1-1-1-1-100-12-1-1-1-12-1-1-10-20-2000-2000-200100-20100010100010
χ31222-122-1222-2-12-1-1-1-12-1-1-1-2-122-2-22-2-121-2-12-1-1-11-211-2-211111100-12-1-1-11-211102020002000-200-100-20-1000-10100010
χ32222-122-1222-2-12-1-1-1-12-1-1-1-2-122-2-22-2-121-2-12-1-1-11-211-2-211111100-12-1-1-11-21110-20-2000-200020010020100010-1000-10
χ33222-122-122-22-12-1-1-1-12-1-1-1-2-122-2-2-221-2-12-12-1-1-11-211-2-2111111001-2111-12-1-1-10202000-2000200-100-20-100010-100010
χ34222-122-122-22-12-1-1-1-12-1-1-1-2-122-2-2-221-2-12-12-1-1-11-211-2-2111111001-2111-12-1-1-10-20-20002000-200100201000-101000-10
χ35222-122-122-2-2-12-1-1-1-12-1-1-12-12222-2-21-21-2-12-1-1-1-12-1-122-1-1-1-1-1-1001-21111-21110202000-2000-200-10020-1000101000-10
χ36222-122-122-2-2-12-1-1-1-12-1-1-12-12222-2-21-21-2-12-1-1-1-12-1-122-1-1-1-1-1-1001-21111-21110-20-20002000200100-201000-10-100010
χ3722-122222-122-1-12-1-1-1-12-1-1222-1-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-122-1-12-1-1-1-12-1-120000-1-1002200-10020000-1-10000-1-100
χ3822-122222-122-1-12-1-1-1-12-1-1222-1-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-1-2-2-1-12-1-1-1-12-1-1-200001100-2-200100-200001100001100
χ3922-122222-12-2-1-12-1-1-1-12-1-1-222-111-1122-2-2-1-12-1-1-2-21111-2-2111122-1-12-1-111-21120000-1-1002-200-100-20000110000-1100
χ4022-122222-12-2-1-12-1-1-1-12-1-1-222-111-1122-2-2-1-12-1-1-2-21111-2-21111-2-2-1-12-1-111-211-200001100-220010020000-1-100001-100
χ4122-122222-1-22-1-12-1-1-1-12-1-1-222-1111-1-2-222-1-12-1-1-2-21111-2-211112211-211-1-12-1-120000-1-100-2200-100-200001100001-100
χ4222-122222-1-22-1-12-1-1-1-12-1-1-222-1111-1-2-222-1-12-1-1-2-21111-2-21111-2-211-211-1-12-1-1-2000011002-20010020000-1-10000-1100
χ4322-122222-1-2-2-1-12-1-1-1-12-1-1222-1-1-111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-12211-21111-21120000-1-100-2-200-10020000-1-100001100
χ4422-122222-1-2-2-1-12-1-1-1-12-1-1222-1-1-111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-2-211-21111-211-2000011002200100-20000110000-1-100
χ454444-2-44-24004-2-2-2-24-2-2-2-20-42-400000000-422220000000000000000000000000040-40000000000-2000020000000000
χ464444-2-44-24004-2-2-2-24-2-2-2-20-42-400000000-4222200000000000000000000000000-404000000000020000-20000000000
χ47444-24-4-24400-24-2-2-2-24-2-2-202-4-4000000002-4222000000000000000000000000040-40000000000-20000200000000000
χ48444-24-4-24400-24-2-2-2-24-2-2-202-4-4000000002-42220000000000000000000000000-404000000000020000-200000000000
χ49444-2-24-2-2444-2-2111-2-21114-2-244444-2-2-2-2-2-2111-2-2-2-2-2-211111100-2-2111-2-21110000000000000000000000000000000
χ50444-2-24-2-244-4-2-2111-2-2111-4-2-24-4-44-4-2-222-2-2111222222-1-1-1-1-1-100-2-211122-1-1-10000000000000000000000000000000
χ51444-2-24-2-24-44-2-2111-2-2111-4-2-24-4-4-4422-2-2-2-2111222222-1-1-1-1-1-10022-1-1-1-2-21110000000000000000000000000000000
χ52444-2-24-2-24-4-4-2-2111-2-21114-2-2444-4-42222-2-2111-2-2-2-2-2-21111110022-1-1-122-1-1-10000000000000000000000000000000
χ5344-244-444-200-2-24-2-2-2-24-2-20-4-420000000022-422000000000000440000000000-40000-2-2000000200000000000000000
χ5444-244-444-200-2-24-2-2-2-24-2-20-4-420000000022-422000000000000-4-400000000004000022000000-200000000000000000
χ5544-24-244-2-244-21-211-21-21144-2-2-2-2-2-24-24-2-21-2114-2-2-211-2-2111100-21-211-21-2110000000000000000000000000000000
χ5644-24-244-2-24-4-21-211-21-211-44-2-222-224-2-42-21-211-4222-1-122-1-1-1-100-21-2112-12-1-10000000000000000000000000000000
χ5744-24-244-2-2-44-21-211-21-211-44-2-2222-2-424-2-21-211-4222-1-122-1-1-1-1002-12-1-1-21-2110000000000000000000000000000000
χ5844-24-244-2-2-4-4-21-211-21-21144-2-2-2-222-42-42-21-2114-2-2-211-2-21111002-12-1-12-12-1-10000000000000000000000000000000
χ5944-2-244-24-2441-2-2111-2-2114-24-2-2-2-2-2-24-241-2-211-2411-2-2-2-21111001-2-2111-2-2110000000000000000000000000000000
χ6044-2-244-24-24-41-2-2111-2-211-4-24-222-22-242-41-2-2112-4-1-12222-1-1-1-1001-2-211-122-1-10000000000000000000000000000000
χ6144-2-244-24-2-441-2-2111-2-211-4-24-2222-22-4-241-2-2112-4-1-12222-1-1-1-100-122-1-11-2-2110000000000000000000000000000000
χ6244-2-244-24-2-4-41-2-2111-2-2114-24-2-2-2222-42-41-2-211-2411-2-2-2-2111100-122-1-1-122-1-10000000000000000000000000000000
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+3i3200111−1−3i32−1+3i32111−1−3i32−1+3i320000000000000000000000000000000
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+3i32−1−3i32−1−3i3200111−1+3i32−1−3i32111−1+3i32−1−3i320000000000000000000000000000000
χ6544-2-2-24-2-2-24-4111−1−3i32−1+3i32111−1−3i32−1+3i32-4-2-2-222-22-2-222111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i3200111−1−3i32−1+3i32-1-1-11+3i321−3i320000000000000000000000000000000
χ6644-2-2-24-2-2-24-4111−1+3i32−1−3i32111−1+3i32−1−3i32-4-2-2-222-22-2-222111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i3200111−1+3i32−1−3i32-1-1-11−3i321+3i320000000000000000000000000000000
χ6744-2-2-24-2-2-2-44111−1−3i32−1+3i32111−1−3i32−1+3i32-4-2-2-2222-222-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i3200-1-1-11+3i321−3i32111−1−3i32−1+3i320000000000000000000000000000000
χ6844-2-2-24-2-2-2-44111−1+3i32−1−3i32111−1+3i32−1−3i32-4-2-2-2222-222-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i3200-1-1-11−3i321+3i32111−1+3i32−1−3i320000000000000000000000000000000
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+3i3200-1-1-11+3i321−3i32-1-1-11+3i321−3i320000000000000000000000000000000
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+3i32−1−3i32−1−3i3200-1-1-11−3i321+3i32-1-1-11−3i321+3i320000000000000000000000000000000
χ714-44440-4-4-40044444-4-4-4-4-4000000000000000000000000000004i−4i0000000000000004i−4i000000000000000000000000
χ724-44440-4-4-40044444-4-4-4-4-400000000000000000000000000000−4i4i000000000000000−4i4i000000000000000000000000
χ734-4-2440-4-4200-2-24-2-222-4220000i6−i60000000000000i6−i6i6−i600i6−i6i6−i64i−4i000000000000000−2i2i000000000000006−600000000
χ744-4-2440-4-4200-2-24-2-222-4220000i6−i60000000000000i6−i6i6−i600i6−i6i6−i6−4i4i0000000000000002i−2i00000000000000−6600000000
χ754-4-2440-4-4200-2-24-2-222-4220000−i6i60000000000000−i6i6−i6i600−i6i6−i6i64i−4i000000000000000−2i2i00000000000000−6600000000
χ764-4-2440-4-4200-2-24-2-222-4220000−i6i60000000000000−i6i6−i6i600−i6i6−i6i6−4i4i0000000000000002i−2i000000000000006−600000000
χ77888-4-4-8-4-4800-4-4222-4-4222044-80000000044-2-2-20000000000000000000000000000000000000000000000000000000
χ7888-48-4-88-4-400-42-422-42-4220-844000000004-24-2-20000000000000000000000000000000000000000000000000000000
χ7988-4-48-8-48-4002-4-4222-4-42204-8400000000-244-2-20000000000000000000000000000000000000000000000000000000
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
χ828-888-40-84-8008-4-4-4-4-84444000000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-4804-8-800-48-4-4-44-8444000000000000000000000000000000000000000000000000000000000000000000000000
χ848-88-4-4044-800-4-422244-2-2-20000000000000000000000032−3232−32−32320000000000000000000000000000000000000000000
χ858-88-4-4044-800-4-422244-2-2-200000000000000000000000−3232−323232−320000000000000000000000000000000000000000000
χ868-8-48-40-84400-42-4224-24-2-200002i6−2i600000000000002i6−2i6−i6i600−i6i6−i6i60000000000000000000000000000000000000000000
χ878-8-48-40-84400-42-4224-24-2-20000−2i62i60000000000000−2i62i6i6−i600i6−i6i6−i60000000000000000000000000000000000000000000
χ888-8-4-4804-84002-4-422-244-2-200002i6−2i60000000000000−i6i62i6−2i600−i6i6−i6i60000000000000000000000000000000000000000000
χ898-8-4-4804-84002-4-422-244-2-20000−2i62i60000000000000i6−i6−2i62i600i6−i6i6−i60000000000000000000000000000000000000000000
χ908-8-4-4-4044400222−1−3i3−1+3i3-2-2-21+3i31−3i300002i6−2i60000000000000−i6i6−i6i6−3232−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+3i31−3i30000−2i62i60000000000000i6−i6i6−i632−32ζ5−2ζ7+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+3i300002i6−2i60000000000000−i6i6−i6i632−322ζ5−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+3i30000−2i62i60000000000000i6−i6i6−i6−3232−2ζ5+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.