Finite Group Databasebeta

← Group #13167040

Character table — Group #13167040

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444444448888888888888812121212121212121212121218181818181818182424242424242424242424243636363636363636363636363636108108108108
order1222344666333366666666666612121212121236661212121212121212121244441212121212121212224466661212121212121212121212124444121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1
χ611111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111
χ811111-1-11111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1111111-1-1
χ91-1-1111-1-1-111111-1-1-1-1-1-11111-1-11-111-1-11-1-11111-1-1-111-1-11-11-111-1-111-1-11-11-111-1-1111-1-1-1111-1-1-1i−ii−i1-1ii−i−iii−i−ii−ii−i
χ101-1-1111-1-1-111111-1-1-1-1-1-11111-1-11-111-1-11-1-11111-1-1-111-1-11-11-111-1-111-1-11-11-111-1-1111-1-1-1111-1-1-1−ii−ii1-1−i−iii−i−iii−ii−ii
χ111-1-1111-1-1-111111-1-1-1-1-1-11111-1-11-111-1-11-1-11111-1-1-111-1-1-11-11-1-111-1-1111-11-111-1-1-1-1-1111-1-1-1111i−ii−i1-1ii−i−iii−i−i−ii−ii
χ121-1-1111-1-1-111111-1-1-1-1-1-11111-1-11-111-1-11-1-11111-1-1-111-1-1-11-11-1-111-1-1111-11-111-1-1-1-1-1111-1-1-1111−ii−ii1-1−i−iii−i−iiii−ii−i
χ131-1-111-11-1-111111-1-1-1-1-1-11111-1-1-11-1-1111-1-11-1-1-1111-1-1111-1-1111-1-1-1-111-111-1-1-111111-1-1-1-1-1-1111i−i−ii1-1ii−i−i−i−iiii−i−ii
χ141-1-111-11-1-111111-1-1-1-1-1-11111-1-1-11-1-1111-1-11-1-1-1111-1-1111-1-1111-1-1-1-111-111-1-1-111111-1-1-1-1-1-1111−iii−i1-1−i−iiiii−i−i−iii−i
χ151-1-111-11-1-111111-1-1-1-1-1-11111-1-1-11-1-1111-1-11-1-1-1111-1-111-111-1-1-11111-1-1-111-1-1-111-1-1-1111111-1-1-1i−i−ii1-1ii−i−i−i−iii−iii−i
χ161-1-111-11-1-111111-1-1-1-1-1-11111-1-1-11-1-1111-1-11-1-1-1111-1-111-111-1-1-11111-1-1-111-1-1-111-1-1-1111111-1-1-1−iii−i1-1−i−iiiii−i−ii−i−ii
χ172222222222222222222222222222222222222222222222000000000000-2-2-2-2-2-2-2-20000000000000000-2-2000000000000
χ1822222-2-22222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000000022-2-222220000000000000000-2-2000000000000
χ192222-122-1-1-122-1-122-1-1-1-122-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i3-2-2-2-211110−i3i30−i3i30−i3i30−i3i3000011000000000000
χ202222-122-1-1-122-1-122-1-1-1-122-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i3-2-2-2-211110i3−i30i3−i30i3−i30i3−i3000011000000000000
χ212222-122-1-1-122-1-122-1-1-1-122-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-12-1-12-1-12-1-12-1-10000-1-1000000000000
χ222222-122-1-1-122-1-122-1-1-1-122-1-122-1-12222-1-1-1-12-1-12-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-211-211-211-2110000-1-1000000000000
χ232222-1-2-2-1-1-122-1-122-1-1-1-122-1-12211-2-2-2-2-1-1-1-1-211-21111110000−i3i3−i3i3i3−i3i3−i322-2-2-1-1-1-10−i3i30−i3i30i3−i30i3−i3000011000000000000
χ242222-1-2-2-1-1-122-1-122-1-1-1-122-1-12211-2-2-2-2-1-1-1-1-211-21111110000i3−i3i3−i3−i3i3−i3i322-2-2-1-1-1-10i3−i30i3−i30−i3i30−i3i3000011000000000000
χ252222-1-2-2-1-1-122-1-122-1-1-1-122-1-12211-2-2-2-2-1-1-1-1-211-211111122-2-2-1-1-1-11111-2-22211112-1-12-1-1-211-2110000-1-1000000000000
χ262222-1-2-2-1-1-122-1-122-1-1-1-122-1-12211-2-2-2-2-1-1-1-1-211-2111111-2-2221111-1-1-1-1-2-2221111-211-2112-1-12-1-10000-1-1000000000000
χ272-2-2222-2-2-222222-2-2-2-2-2-22222-2-22-222-2-22-2-22222-2-2-222-2-2000000000000-22-22-2-2220000000000000000-22000000000000
χ282-2-222-22-2-222222-2-2-2-2-2-22222-2-2-22-2-2222-2-22-2-2-2222-2-2220000000000002-2-2222-2-20000000000000000-22000000000000
χ292-2-22-12-211-122-1-1-2-2111122-1-1-2-2-1122-2-2-111-12-1-1-211-1-1110000−i3i3i3−i3−i3i3i3−i3-22-2211-1-10−i3i30i3−i30−i3i30i3−i300001-1000000000000
χ302-2-22-12-211-122-1-1-2-2111122-1-1-2-2-1122-2-2-111-12-1-1-211-1-1110000i3−i3−i3i3i3−i3−i3i3-22-2211-1-10i3−i30−i3i30i3−i30−i3i300001-1000000000000
χ312-2-22-12-211-122-1-1-2-2111122-1-1-2-2-1122-2-2-111-12-1-1-211-1-1112-22-2-1-111-1-1112-22-2-1-1112-1-1-2112-1-1-2110000-11000000000000
χ322-2-22-12-211-122-1-1-2-2111122-1-1-2-2-1122-2-2-111-12-1-1-211-1-111-22-2211-1-111-1-12-22-2-1-111-2112-1-1-2112-1-10000-11000000000000
χ332-2-22-1-2211-122-1-1-2-2111122-1-1-2-21-1-2-222-111-1-2112-1-111-1-10000−i3i3i3−i3i3−i3−i3i32-2-22-1-1110−i3i30i3−i30i3−i30−i3i300001-1000000000000
χ342-2-22-1-2211-122-1-1-2-2111122-1-1-2-21-1-2-222-111-1-2112-1-111-1-10000i3−i3−i3i3−i3i3i3−i32-2-22-1-1110i3−i30−i3i30−i3i30i3−i300001-1000000000000
χ352-2-22-1-2211-122-1-1-2-2111122-1-1-2-21-1-2-222-111-1-2112-1-111-1-12-2-22-1-11111-1-1-222-211-1-12-1-1-211-2112-1-10000-11000000000000
χ362-2-22-1-2211-122-1-1-2-2111122-1-1-2-21-1-2-222-111-1-2112-1-111-1-1-222-211-1-1-1-111-222-211-1-1-2112-1-12-1-1-2110000-11000000000000
χ3744444444441-211111111-2111-2-244-2-2-2-2-2-2-2-2111111-2-2-2-222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3844444444441-211111111-2111-2-244-2-2-2-2-2-2-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000111111111111000000000000000000
χ394444444444-21-2-2-2-2-2-2-2-21-2-2-2114411111111-2-2-2-2-2-2111100000000000000000000000000000000222200-1-1-1-1-1-1-1-10000
χ404444444444-21-2-2-2-2-2-2-2-21-2-2-2114411111111-2-2-2-2-2-2111100000000000000000000000000000000-2-2-2-200111111110000
χ4144444-4-44441-211111111-2111-2-2-4-42222-2-2-2-2-1-1-1-1-1-1222222-2-22222-2-2-2-200000000-1-1-1-1-1-1111111000000000000000000
χ4244444-4-44441-211111111-2111-2-2-4-42222-2-2-2-2-1-1-1-1-1-12222-2-222-2-2-2-2222200000000111111-1-1-1-1-1-1000000000000000000
χ4344444-4-4444-21-2-2-2-2-2-2-2-21-2-2-211-4-4-1-1-1-11111222222-1-1-1-10000000000000000000000000000000022-2-200-1-1-1-111110000
χ4444444-4-4444-21-2-2-2-2-2-2-2-21-2-2-211-4-4-1-1-1-11111222222-1-1-1-100000000000000000000000000000000-2-222001111-1-1-1-10000
χ454444-244-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2-2-2-2-211111−1−3i32−1+3i321−1−3i32−1+3i3211112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300000000-11+i321−i32-11+i321−i32-11+i321−i32-11+i321−i32000000000000000000
χ464444-244-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-2-2-2-2-2-2-2-211111−1−3i32−1+3i321−1−3i32−1+3i321111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i3000000001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ474444-244-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2-2-2-2-211111−1+3i32−1−3i321−1+3i32−1−3i3211112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300000000-11−i321+i32-11−i321+i32-11−i321+i32-11−i321+i32000000000000000000
χ484444-244-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-2-2-2-2-2-2-2-211111−1+3i32−1−3i321−1+3i32−1−3i321111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i3000000001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ494444-2-4-4-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-2-22222221111-11+3i321−3i32-11+3i321−3i32-1-1-1-122-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300000000-11+i321−i32-11+i321−i321−1−i32−1+i321−1−i32−1+i32000000000000000000
χ504444-2-4-4-2-2-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-21−1−3i32−1+3i32-2-22222221111-11+3i321−3i32-11+3i321−3i32-1-1-1-1-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3000000001−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32000000000000000000
χ514444-2-4-4-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-2-22222221111-11−3i321+3i32-11−3i321+3i32-1-1-1-122-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300000000-11−i321+i32-11−i321+i321−1+i32−1−i321−1+i32−1−i32000000000000000000
χ524444-2-4-4-2-2-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-21−1+3i32−1−3i32-2-22222221111-11−3i321+3i32-11−3i321+3i32-1-1-1-1-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3000000001−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32000000000000000000
χ5344-4-44004-4-444444-44-44-4-4-4-4-44-400000044-4-4000000000000000000000000000000000000000000000000000000000000
χ5444-4-44004-4-4-21-2-2-22-22-22-12221-1003i−3i3i−3i11-1-10000003i−3i3i−3i00000000000000000000000000000000000000−i3i3−i3i33−33−30000
χ5544-4-44004-4-4-21-2-2-22-22-22-12221-1003i−3i3i−3i11-1-10000003i−3i3i−3i00000000000000000000000000000000000000i3−i3i3−i3−33−330000
χ5644-4-44004-4-4-21-2-2-22-22-22-12221-100−3i3i−3i3i11-1-1000000−3i3i−3i3i00000000000000000000000000000000000000−i3i3−i3i3−33−330000
χ5744-4-44004-4-4-21-2-2-22-22-22-12221-100−3i3i−3i3i11-1-1000000−3i3i−3i3i00000000000000000000000000000000000000i3−i3i3−i33−33−30000
χ5844-4-4-200-22244-2-24-4-22-22-4-4224-4000000-2-22200000000000000000000000000−2i32i3−2i32i3000000000000000000000000000000
χ5944-4-4-200-22244-2-24-4-22-22-4-4224-4000000-2-222000000000000000000000000002i3−2i32i3−2i3000000000000000000000000000000
χ604-44-4400-44-44444-44-44-44-4-4-4-4-440000004-44-4000000000000000000000000000000000000000000000000000000000000
χ614-44-4400-44-4-21-2-22-22-22-2-1222-11003i−3i−3i3i1-11-10000003i−3i−3i3i000000000000000000000000000000000000003−3−33i3−i3−i3i30000
χ624-44-4400-44-4-21-2-22-22-22-2-1222-11003i−3i−3i3i1-11-10000003i−3i−3i3i00000000000000000000000000000000000000−333−3−i3i3i3−i30000
χ634-44-4400-44-4-21-2-22-22-22-2-1222-1100−3i3i3i−3i1-11-1000000−3i3i3i−3i000000000000000000000000000000000000003−3−33−i3i3i3−i30000
χ644-44-4400-44-4-21-2-22-22-22-2-1222-1100−3i3i3i−3i1-11-1000000−3i3i3i−3i00000000000000000000000000000000000000−333−3i3−i3−i3i30000
χ654-44-4-2002-2244-2-2-442-22-2-4-422-44000000-22-2200000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000
χ664-44-4-2002-2244-2-2-442-22-2-4-422-44000000-22-22000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000
χ674-4-4444-4-4-441-211-1-1-1-1-1-1-2111224-4-2-222-222-2111-1-1-1-2-2222-22-222-2-222-2-200000000-1-1-1111-1-1-1111000000000000000000
χ684-4-4444-4-4-441-211-1-1-1-1-1-1-2111224-4-2-222-222-2111-1-1-1-2-222-22-22-2-222-2-22200000000111-1-1-1111-1-1-1000000000000000000
χ694-4-4444-4-4-44-21-2-22222221-2-2-2-1-14-411-1-11-1-11-2-2-222211-1-1000000000000000000000000000000002i−2i2i−2i00−i−iii−i−iii0000
χ704-4-4444-4-4-44-21-2-22222221-2-2-2-1-14-411-1-11-1-11-2-2-222211-1-100000000000000000000000000000000−2i2i−2i2i00ii−i−iii−i−i0000
χ714-4-444-44-4-441-211-1-1-1-1-1-1-211122-4422-2-2-222-2-1-1-111122-2-22-2-2222-2-2-2-22200000000-1-1-1111111-1-1-1000000000000000000
χ724-4-444-44-4-441-211-1-1-1-1-1-1-211122-4422-2-2-222-2-1-1-111122-2-2-222-2-2-22222-2-200000000111-1-1-1-1-1-1111000000000000000000
χ734-4-444-44-4-44-21-2-22222221-2-2-2-1-1-44-1-1111-1-11222-2-2-2-1-111000000000000000000000000000000002i−2i−2i2i00−i−iiiii−i−i0000
χ744-4-444-44-4-44-21-2-22222221-2-2-2-1-1-44-1-1111-1-11222-2-2-2-1-11100000000000000000000000000000000−2i2i2i−2i00ii−i−i−i−iii0000
χ754-4-44-24-422-21-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i3222-22-2-2221-1-111−1−3i32−1+3i32-11+3i321−3i3211-1-12-22-2−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i300000000-11+i321−i321−1−i32−1+i32-11+i321−i321−1−i32−1+i32000000000000000000
χ764-4-44-24-422-21-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i3222-22-2-2221-1-111−1−3i32−1+3i32-11+3i321−3i3211-1-1-22-221+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3000000001−1−i32−1+i32-11+i321−i321−1−i32−1+i32-11+i321−i32000000000000000000
χ774-4-44-24-422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i3222-22-2-2221-1-111−1+3i32−1−3i32-11−3i321+3i3211-1-12-22-2−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i300000000-11−i321+i321−1+i32−1−i32-11−i321+i321−1+i32−1−i32000000000000000000
χ784-4-44-24-422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i3222-22-2-2221-1-111−1+3i32−1−3i32-11−3i321+3i3211-1-1-22-221−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3000000001−1+i32−1−i32-11−i321+i321−1+i32−1−i32-11−i321+i32000000000000000000
χ794-4-44-2-4422-21-2−1−3i32−1+3i32-1-11+3i321+3i321−3i321−3i32-21−1−3i32−1+3i32222-222-2-21-1-11-11+3i321−3i321−1−3i32−1+3i32-1-1112-2-22−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i300000000-11+i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32000000000000000000
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χ814-4-44-2-4422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i32222-222-2-21-1-11-11−3i321+3i321−1+3i32−1−3i32-1-1112-2-22−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i300000000-11−i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32000000000000000000
χ824-4-44-2-4422-21-2−1+3i32−1−3i32-1-11−3i321−3i321+3i321+3i32-21−1+3i32−1−3i32222-222-2-21-1-11-11−3i321+3i321−1+3i32−1−3i32-1-111-222-21−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3000000001−1+i32−1−i32-11−i321+i32-11−i321+i321−1+i32−1−i32000000000000000000
χ838888-488-4-4-4-4222-4-422222-42222-4-42222-1-1-1-1-422-422-1-1-1-100000000000000000000000000000000000000000000000000
χ848888-4-8-8-4-4-4-4222-4-422222-4222244-2-2-2-2-1-1-1-14-2-24-2-2111100000000000000000000000000000000000000000000000000
χ8588-8-88008-8-82-4222-22-22-24-2-2-2-44000000-4-444000000000000000000000000000000000000000000000000000000000000
χ8688-8-8-400-4442-4−1−3i3−1+3i32-2−1−3i31+3i3−1+3i31−3i34-21+3i31−3i3-4400000022-2-2000000000000000000000000000000000000000000000000000000000000
χ8788-8-8-400-4442-4−1+3i3−1−3i32-2−1+3i31−3i3−1−3i31+3i34-21−3i31+3i3-4400000022-2-2000000000000000000000000000000000000000000000000000000000000
χ8888-8-8-400-444-4222-442-22-2-24-2-22-2006i−6i6i−6i-1-111000000−3i3i−3i3i00000000000000000000000000000000000000000000000000
χ8988-8-8-400-444-4222-442-22-2-24-2-22-200−6i6i−6i6i-1-1110000003i−3i3i−3i00000000000000000000000000000000000000000000000000
χ908-88-8800-88-82-422-22-22-224-2-2-24-4000000-44-44000000000000000000000000000000000000000000000000000000000000
χ918-88-8-4004-442-4−1−3i3−1+3i3-221+3i3−1−3i31−3i3−1+3i34-21+3i31−3i34-40000002-22-2000000000000000000000000000000000000000000000000000000000000
χ928-88-8-4004-442-4−1+3i3−1−3i3-221−3i3−1+3i31+3i3−1−3i34-21−3i31+3i34-40000002-22-2000000000000000000000000000000000000000000000000000000000000
χ938-88-8-4004-44-42224-4-22-22-24-2-2-22006i−6i−6i6i-11-11000000−3i3i3i−3i00000000000000000000000000000000000000000000000000
χ948-88-8-4004-44-42224-4-22-22-24-2-2-2200−6i6i6i−6i-11-110000003i−3i−3i3i00000000000000000000000000000000000000000000000000
χ958-8-88-48-844-4-422244-2-2-2-22-422-2-2-4422-2-2-111-1-4224-2-2-1-11100000000000000000000000000000000000000000000000000
χ968-8-88-4-8844-4-422244-2-2-2-22-422-2-24-4-2-222-111-14-2-2-42211-1-100000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).