Finite Group Databasebeta

← Group #13167231

Character table — Group #13167231

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11222444444444444888888888888121212121212121212121212121212121212161616161818242424242424242424363636363672727272108108144216
order12346233336666661236666666121212122224666666666666121266612246666661212124612121248242444128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111111-1-11-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-111-11
χ511111-11111-1-1111111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-11-1-1-1111-1
χ611111-11111-1-1111111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1111-1-1-11
χ711111-11111-1-1111111-1-1-1-1-1-111111-1-111-1-1-1-11111111111-1-1-1111-1-1-1-1-1-1111-111-1-11-1-1-1-1-111
χ811111-11111-1-1111111-1-1-1-1-1-111111-1-111-1-1-1-11111111111-1-1-1111-1-1-1-1-1-1111-111-1-1-111111-1-1
χ9222222222222222222222222222220000000000000000002222-2-2000000000-2-2-2-2-200000000
χ1022222-22222-2-2222222-2-2-2-2-2-222222000000000000000000-2-2-22-2-20000000002-2-22200000000
χ11222-2202222002222-220000002-2-2-2-2002-2000022222222-2-2000-2-22000000-2-2-20-220000000000
χ12222-2202222002222-220000002-2-2-2-200-220000-2-2-2-2-2-2-2-222000-2-220000002220-220000000000
χ13222-2202222002222-220000002-2-2-2-22-20022-2-20000000000000-22-2222-2-2-200002-20000000000
χ14222-2202222002222-220000002-2-2-2-2-2200-2-2220000000000000-22-2-2-2-222200002-20000000000
χ1522-12-1222-1-1-1-12-1-12-1-122-1-1-1-1-12-1-120000−i3i3−i3i3−i3i300−i3−i3i3i3−i3i32-1-1-1-2-20−i3i30−i3i30−i3i3-2111100000000
χ1622-12-1222-1-1-1-12-1-12-1-122-1-1-1-1-12-1-120000i3−i3i3−i3i3−i300i3i3−i3−i3i3−i32-1-1-1-2-20i3−i30i3−i30i3−i3-2111100000000
χ1722-12-1222-1-1-1-12-1-12-1-122-1-1-1-1-12-1-122222-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-1-12-1-12-1-12-1-1-1-100000000
χ1822-12-1222-1-1-1-12-1-12-1-122-1-1-1-1-12-1-12-2-2-2-2111111-2-21111112-1-1-122-211-211-2112-1-1-1-100000000
χ1922-12-1-222-1-1112-1-12-1-1-2-21111-12-1-120000−i3i3−i3i3i3−i300i3i3−i3−i3i3−i3-211-1-2-20−i3i30−i3i30i3−i3211-1-100000000
χ2022-12-1-222-1-1112-1-12-1-1-2-21111-12-1-120000i3−i3i3−i3−i3i300−i3−i3i3i3−i3i3-211-1-2-20i3−i30i3−i30−i3i3211-1-100000000
χ2122-12-1-222-1-1112-1-12-1-1-2-21111-12-1-1222-2-2-1-1-1-111-2-2111111-211-1222-1-12-1-1-211-2-1-11100000000
χ2222-12-1-222-1-1112-1-12-1-1-2-21111-12-1-12-2-2221111-1-122-1-1-1-1-1-1-211-122-211-2112-1-1-2-1-11100000000
χ2322-1-2-1022-1-1−i3i32-1-121-100−i3−i3i3i3-1-211-2002-2−i3i3i3−i3-1-122-1-1-1-1110−i3i31-220−i3i30i3−i3-21101-1−i3i300000000
χ2422-1-2-1022-1-1−i3i32-1-121-100−i3−i3i3i3-1-211-200-22i3−i3−i3i311-2-21111-1-10−i3i31-220i3−i30−i3i32-1-101-1−i3i300000000
χ2522-1-2-1022-1-1−i3i32-1-121-100−i3−i3i3i3-1-211-22-200-1-111−i3i300−i3−i3i3i3i3−i30−i3i312-22-1-1-2110i3−i30-11i3−i300000000
χ2622-1-2-1022-1-1−i3i32-1-121-100−i3−i3i3i3-1-211-2-220011-1-1i3−i300i3i3−i3−i3−i3i30−i3i312-2-2112-1-10−i3i30-11i3−i300000000
χ2722-1-2-1022-1-1i3−i32-1-121-100i3i3−i3−i3-1-211-2002-2i3−i3−i3i3-1-122-1-1-1-1110i3−i31-220i3−i30−i3i3-21101-1i3−i300000000
χ2822-1-2-1022-1-1i3−i32-1-121-100i3i3−i3−i3-1-211-200-22−i3i3i3−i311-2-21111-1-10i3−i31-220−i3i30i3−i32-1-101-1i3−i300000000
χ2922-1-2-1022-1-1i3−i32-1-121-100i3i3−i3−i3-1-211-22-200-1-111i3−i300i3i3−i3−i3−i3i30i3−i312-22-1-1-2110−i3i30-11−i3i300000000
χ3022-1-2-1022-1-1i3−i32-1-121-100i3i3−i3−i3-1-211-2-220011-1-1−i3i300−i3−i3i3i3i3−i30i3−i312-2-2112-1-10i3−i30-11−i3i300000000
χ314444441-2-2-244-2-2-2141-2-2-2-2-2-21-2-2-210000000000000000001111000000000000000022-1-100-10
χ324444441-2-2-244-2-2-2141-2-2-2-2-2-21-2-2-2100000000000000000011110000000000000000-2-2110010
χ33444444-211144111-24-2111111-2111-22222222222-1-1-1-1-1-122-2-2-2-200-1-1-1-1-1-1-1-1-10000000000000
χ34444444-211144111-24-2111111-2111-2-2-2-2-2-2-2-2-2-2-2111111-2-2-2-2-2-2001111111110000000000000
χ3544444-41-2-2-2-4-4-2-2-21412222221-2-2-21000000000000000000-1-1-1100000000000000002-21100-10
χ3644444-41-2-2-2-4-4-2-2-21412222221-2-2-21000000000000000000-1-1-110000000000000000-22-1-10010
χ3744444-4-2111-4-4111-24-2-1-1-1-1-1-1-2111-222-2-22222-2-2111111-2-2222-200-1-1-1-1-1-11110000000000000
χ3844444-4-2111-4-4111-24-2-1-1-1-1-1-1-2111-2-2-222-2-2-2-222-1-1-1-1-1-122222-200111111-1-1-10000000000000
χ39444-440-211100111-2-4-23-33-33-3-2-1-1-122-22-222-2-222-1-1-1-1-1-1-2-2000200-1-1-11111110000000000000
χ40444-440-211100111-2-4-23-33-33-3-2-1-1-12-22-22-2-222-2-211111122000200111-1-1-1-1-1-10000000000000
χ41444-440-211100111-2-4-2-33-33-33-2-1-1-122-2-2222-2-2-2-211111122000200-1-1-1111-1-1-10000000000000
χ42444-440-211100111-2-4-2-33-33-33-2-1-1-12-222-2-2-22222-1-1-1-1-1-1-2-2000200111-1-1-11110000000000000
χ4344-24-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2111−1−3i32−1+3i32−1+3i32−1−3i3211−1−3i32−1+3i32-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3-211100-11+i321−i32-11+i321−i32-11+i321−i320000000000000
χ4444-24-24-21−1−3i32−1+3i32-2-21−1−3i32−1+3i32-2-2111−1−3i32−1+3i32−1+3i32−1−3i3211−1−3i32−1+3i32-2-2-2-2-21+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i3-2111001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i320000000000000
χ4544-24-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2111−1+3i32−1−3i32−1−3i32−1+3i3211−1+3i32−1−3i32-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3-211100-11−i321+i32-11−i321+i32-11−i321+i320000000000000
χ4644-24-24-21−1+3i32−1−3i32-2-21−1+3i32−1−3i32-2-2111−1+3i32−1−3i32−1−3i32−1+3i3211−1+3i32−1−3i32-2-2-2-2-21−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i3-2111001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i320000000000000
χ4744-24-2-4-21−1−3i32−1+3i32221−1−3i32−1+3i32-2-21-1-11+3i321−3i321−3i321+3i3211−1−3i32−1+3i32-222-2-2−1−i3−1+i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i32-1-1100-11+i321−i32-11+i321−i321−1−i32−1+i320000000000000
χ4844-24-2-4-21−1−3i32−1+3i32221−1−3i32−1+3i32-2-21-1-11+3i321−3i321−3i321+3i3211−1−3i32−1+3i32-2-2-2221+i31−i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i32-1-11001−1−i32−1+i321−1−i32−1+i32-11+i321−i320000000000000
χ4944-24-2-4-21−1+3i32−1−3i32221−1+3i32−1−3i32-2-21-1-11−3i321+3i321+3i321−3i3211−1+3i32−1−3i32-222-2-2−1+i3−1−i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i32-1-1100-11−i321+i32-11−i321+i321−1+i32−1−i320000000000000
χ5044-24-2-4-21−1+3i32−1−3i32221−1+3i32−1−3i32-2-21-1-11−3i321+3i321+3i321−3i3211−1+3i32−1−3i32-2-2-2221−i31+i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i32-1-11001−1+i32−1−i321−1+i32−1−i32-11−i321+i320000000000000
χ5144-2-4-20-21−1−3i32−1+3i32−2i32i31−1−3i32−1+3i32-2213-3−3−i323−i32−3+i323+i321-11+3i321−3i3222-22-2−1−i3−1+i31+i31−i3−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i30i3−i3-100-11+i321−i321−1−i32−1+i321−1−i32−1+i320000000000000
χ5244-2-4-20-21−1−3i32−1+3i32−2i32i31−1−3i32−1+3i32-2213-3−3−i323−i32−3+i323+i321-11+3i321−3i322-22-221+i31−i3−1−i3−1+i31+i31−i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i30i3−i3-1001−1−i32−1+i32-11+i321−i32-11+i321−i320000000000000
χ5344-2-4-20-21−1−3i32−1+3i322i3−2i31−1−3i32−1+3i32-221-333+i32−3+i323−i32−3−i321-11+3i321−3i3222-2-22−1−i3−1+i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i32−1−i3−1+i30−i3i3-100-11+i321−i321−1−i32−1+i32-11+i321−i320000000000000
χ5444-2-4-20-21−1−3i32−1+3i322i3−2i31−1−3i32−1+3i32-221-333+i32−3+i323−i32−3−i321-11+3i321−3i322-222-21+i31−i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i30−i3i3-1001−1−i32−1+i32-11+i321−i321−1−i32−1+i320000000000000
χ5544-2-4-20-21−1+3i32−1−3i32−2i32i31−1+3i32−1−3i32-221-333−i32−3−i323+i32−3+i321-11−3i321+3i3222-2-22−1+i3−1−i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i30i3−i3-100-11−i321+i321−1+i32−1−i32-11−i321+i320000000000000
χ5644-2-4-20-21−1+3i32−1−3i32−2i32i31−1+3i32−1−3i32-221-333−i32−3−i323+i32−3+i321-11−3i321+3i322-222-21−i31+i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i30i3−i3-1001−1+i32−1−i32-11−i321+i321−1+i32−1−i320000000000000
χ5744-2-4-20-21−1+3i32−1−3i322i3−2i31−1+3i32−1−3i32-2213-3−3+i323+i32−3−i323−i321-11−3i321+3i3222-22-2−1+i3−1−i31−i31+i3−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i30−i3i3-100-11−i321+i321−1+i32−1−i321−1+i32−1−i320000000000000
χ5844-2-4-20-21−1+3i32−1−3i322i3−2i31−1+3i32−1−3i32-2213-3−3+i323+i32−3−i323−i321-11−3i321+3i322-22-221−i31+i3−1+i3−1−i31−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i30−i3i3-1001−1+i32−1−i32-11−i321+i32-11−i321+i320000000000000
χ594-440-40444400-4-4-4-404000000-400000000000000000000000000000000000000000000002i−2i00
χ604-440-40444400-4-4-4-404000000-40000000000000000000000000000000000000000000000−2i2i00
χ61888-8802-4-4-400-4-4-42-820000002444-2000000000000000000000-2000000000000000000000000
χ6288-48-482-422-4-4-4222-4-1-4-42222-1-42220000000000000000002-1-1-1000000000000000000000000
χ6388-48-4-82-42244-4222-4-144-2-2-2-2-1-4222000000000000000000-211-1000000000000000000000000
χ6488-4-8-402-422−4i34i3-42224-1002i32i3−2i3−2i3-14-2-2-20000000000000000000−i3i31000000000000000000000000
χ6588-4-8-402-4224i3−4i3-42224-100−2i3−2i32i32i3-14-2-2-20000000000000000000i3−i31000000000000000000000000
χ668-880-802-4-4-400444-202000000-2000000000000000000000000000000000000000000006−60000
χ678-880-802-4-4-400444-202000000-200000000000000000000000000000000000000000000−660000
χ688-880-80-422200-2-2-240-4000000400000000000000−2i32i3−2i32i3−2i32i3000000000000000000000000000000
χ698-880-80-422200-2-2-240-40000004000000000000002i3−2i32i3−2i32i3−2i3000000000000000000000000000000
χ708-8-404088-4-400-844-80-4000000400000000000000000000000000000000000000000000000000
χ718-8-4040-42−1−3i3−1+3i300-21+3i31−3i3402000000-200000000000000−2i32i3−3+i33−i33+i3−3−i3000000000000000000000000000000
χ728-8-4040-42−1−3i3−1+3i300-21+3i31−3i3402000000-2000000000000002i3−2i33−i3−3+i3−3−i33+i3000000000000000000000000000000
χ738-8-4040-42−1+3i3−1−3i300-21−3i31+3i3402000000-200000000000000−2i32i33+i3−3−i3−3+i33−i3000000000000000000000000000000
χ748-8-4040-42−1+3i3−1−3i300-21−3i31+3i3402000000-2000000000000002i3−2i3−3−i33+i33−i3−3+i3000000000000000000000000000000
χ7516-16-80804-844008-4-4-40-2000000200000000000000000000000000000000000000000000000000

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