Finite Group Databasebeta

← Group #13147109

Character table — Group #13147109

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222222666666666666121212121212121212121212121212121212121212121212181818182424242424242424242424242424242424242424545454547272727272727272
order122234466612121212444491818183636363633666666121212123636363636363636363636362244991212121218181818181836363636363636364444666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ411111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ611111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ711111-1-1111-1-1-1-1-1-1111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ811111-1-1111-1-1-1-1-1-1111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ911111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-111-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1011111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1111111-1-1-1-1-1-1-1-111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1111111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-111-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1211111-1-1111-1-1-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1111111-1-1-1-1-1-1-1-111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ131-1-111i−i-11-1ii−i−ii−i1-11-11-1ii−i−i1111-1-1-1-11-1i−i111-1-1-1iii−i−i−i1-1i−i11i−ii−i1-11-1-1-1ii−i−iii−i−ii−i1-11-11-1i−ii−i
χ141-1-111i−i-11-1ii−i−ii−i1-11-11-1ii−i−i1111-1-1-1-11-1i−i111-1-1-1iii−i−i−i-11−ii11i−ii−i1-11-1-1-1ii−i−iii−i−i−ii-11-11-11−ii−ii
χ151-1-111i−i-11-1ii−i−ii−i1-11-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1i−i111-1-1-1iii−i−i−i1-1i−i−1−i32−1+i32−ζ15ζ15−ζ3ζ3−1−i321+i32−1+i321−i321+i321−i32−ζ15−ζ15ζ15ζ15−ζ3−ζ3ζ3ζ3i−i1-1−1−i321+i32−1+i321−i32−ζ15ζ15−ζ3ζ3
χ161-1-111i−i-11-1ii−i−ii−i1-11-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1i−i111-1-1-1iii−i−i−i-11−ii−1−i32−1+i32−ζ15ζ15−ζ3ζ3−1−i321+i32−1+i321−i321+i321−i32−ζ15−ζ15ζ15ζ15−ζ3−ζ3ζ3ζ3−ii-111+i32−1−i321−i32−1+i32ζ15−ζ15ζ3−ζ3
χ171-1-111i−i-11-1ii−i−ii−i1-11-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1i−i111-1-1-1iii−i−i−i1-1i−i−1+i32−1−i32−ζ3ζ3−ζ15ζ15−1+i321−i32−1−i321+i321−i321+i32−ζ3−ζ3ζ3ζ3−ζ15−ζ15ζ15ζ15i−i1-1−1+i321−i32−1−i321+i32−ζ3ζ3−ζ15ζ15
χ181-1-111i−i-11-1ii−i−ii−i1-11-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1i−i111-1-1-1iii−i−i−i-11−ii−1+i32−1−i32−ζ3ζ3−ζ15ζ15−1+i321−i32−1−i321+i321−i321+i32−ζ3−ζ3ζ3ζ3−ζ15−ζ15ζ15ζ15−ii-111−i32−1+i321+i32−1−i32ζ3−ζ3ζ15−ζ15
χ191-1-111−ii-11-1−i−iii−ii1-11-11-1−i−iii1111-1-1-1-11-1−ii111-1-1-1−i−i−iiii1-1−ii11−ii−ii1-11-1-1-1−i−iii−i−iii−ii1-11-11-1−ii−ii
χ201-1-111−ii-11-1−i−iii−ii1-11-11-1−i−iii1111-1-1-1-11-1−ii111-1-1-1−i−i−iiii-11i−i11−ii−ii1-11-1-1-1−i−iii−i−iiii−i-11-11-11i−ii−i
χ211-1-111−ii-11-1−i−iii−ii1-11-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−ii111-1-1-1−i−i−iiii1-1−ii−1−i32−1+i32ζ15−ζ15ζ3−ζ3−1−i321+i32−1+i321−i321+i321−i32ζ15ζ15−ζ15−ζ15ζ3ζ3−ζ3−ζ3−ii1-1−1−i321+i32−1+i321−i32ζ15−ζ15ζ3−ζ3
χ221-1-111−ii-11-1−i−iii−ii1-11-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−ii111-1-1-1−i−i−iiii-11i−i−1−i32−1+i32ζ15−ζ15ζ3−ζ3−1−i321+i32−1+i321−i321+i321−i32ζ15ζ15−ζ15−ζ15ζ3ζ3−ζ3−ζ3i−i-111+i32−1−i321−i32−1+i32−ζ15ζ15−ζ3ζ3
χ231-1-111−ii-11-1−i−iii−ii1-11-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1−ii111-1-1-1−i−i−iiii1-1−ii−1+i32−1−i32ζ3−ζ3ζ15−ζ15−1+i321−i32−1−i321+i321−i321+i32ζ3ζ3−ζ3−ζ3ζ15ζ15−ζ15−ζ15−ii1-1−1+i321−i32−1−i321+i32ζ3−ζ3ζ15−ζ15
χ241-1-111−ii-11-1−i−iii−ii1-11-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1−ii111-1-1-1−i−i−iiii-11i−i−1+i32−1−i32ζ3−ζ3ζ15−ζ15−1+i321−i32−1−i321+i321−i321+i32ζ3ζ3−ζ3−ζ3ζ15ζ15−ζ15−ζ15i−i-111−i32−1+i321+i32−1−i32−ζ3ζ3−ζ15ζ15
χ25222222222222222222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ26222222222222222222-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-100001+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321−i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32000000000000
χ27222222222222222222-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-100001−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321+i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32000000000000
χ2822222-2-2222-2-2-2-2-2-222-1-1-1-111112222222222-2-2-1-1-1-1-1-11111110000-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000
χ2922222-2-2222-2-2-2-2-2-222-1-1-1-11111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-2-2-1-1-1-1-1-111111100001+i321−i321+i31+i31−i31−i31+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3022222-2-2222-2-2-2-2-2-222-1-1-1-11111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-2-2-1-1-1-1-1-111111100001−i321+i321−i31−i31+i31+i31−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ312-2-2222i−2i-22-22i2i−2i−2i2i−2i2-2-11-11−i−iii2222-2-2-2-22-22i−2i-1-1-1111−i−i−iiii0000-1-12i−2i2i−2i-11-1111−i−iii−i−iii000000000000
χ322-2-2222i−2i-22-22i2i−2i−2i2i−2i2-2-11-11−i−iii−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-22i−2i-1-1-1111−i−i−iiii00001+i321−i32−2ζ152ζ15−2ζ32ζ31+i32−1−i321−i32−1+i32−1−i32−1+i32ζ15ζ15−ζ15−ζ15ζ3ζ3−ζ3−ζ3000000000000
χ332-2-2222i−2i-22-22i2i−2i−2i2i−2i2-2-11-11−i−iii−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-22i−2i-1-1-1111−i−i−iiii00001−i321+i32−2ζ32ζ3−2ζ152ζ151−i32−1+i321+i32−1−i32−1+i32−1−i32ζ3ζ3−ζ3−ζ3ζ15ζ15−ζ15−ζ15000000000000
χ342-2-222−2i2i-22-2−2i−2i2i2i−2i2i2-2-11-11ii−i−i2222-2-2-2-22-2−2i2i-1-1-1111iii−i−i−i0000-1-1−2i2i−2i2i-11-1111ii−i−iii−i−i000000000000
χ352-2-222−2i2i-22-2−2i−2i2i2i−2i2i2-2-11-11ii−i−i−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-2−2i2i-1-1-1111iii−i−i−i00001+i321−i322ζ15−2ζ152ζ3−2ζ31+i32−1−i321−i32−1+i32−1−i32−1+i32−ζ15−ζ15ζ15ζ15−ζ3−ζ3ζ3ζ3000000000000
χ362-2-222−2i2i-22-2−2i−2i2i2i−2i2i2-2-11-11ii−i−i−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-2−2i2i-1-1-1111iii−i−i−i00001−i321+i322ζ3−2ζ32ζ15−2ζ151−i32−1+i321+i32−1−i32−1+i32−1−i32−ζ3−ζ3ζ3ζ3−ζ15−ζ15ζ15ζ15000000000000
χ3733333333333333-1-1-1-13333333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333300000000000000000000-1-1-1-100000000
χ3833333333333333-1-1-1-13333333300000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-300000000000000000000111100000000
χ3933333-3-3333-3-3-3-311-1-13333-3-3-3-300000000-1-111-1-1-1-1-1-111111133-3-30000000000000000000011-1-100000000
χ4033333-3-3333-3-3-3-311-1-13333-3-3-3-300000000-1-111-1-1-1-1-1-1111111-3-33300000000000000000000-1-11100000000
χ413-3-3333i−3i-33-33i3i−3i−3i−ii-113-33-33i3i−3i−3i00000000-11−ii-1-1-1111−i−i−iiii3-33i−3i00000000000000000000−ii-1100000000
χ423-3-3333i−3i-33-33i3i−3i−3i−ii-113-33-33i3i−3i−3i00000000-11−ii-1-1-1111−i−i−iiii-33−3i3i00000000000000000000i−i1-100000000
χ433-3-333−3i3i-33-3−3i−3i3i3ii−i-113-33-3−3i−3i3i3i00000000-11i−i-1-1-1111iii−i−i−i3-3−3i3i00000000000000000000i−i-1100000000
χ443-3-333−3i3i-33-3−3i−3i3i3ii−i-113-33-3−3i−3i3i3i00000000-11i−i-1-1-1111iii−i−i−i-333i−3i00000000000000000000−ii1-100000000
χ4544-4-4400-4-44000000004-4-440000-2-22222-2-200000000000000000000-2-200002-22-22200000000000000000000
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χ4744-4-4400-4-44000000004-4-4400001−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000000000001−i31+i30000−1+i31−i3−1−i31+i3−1+i3−1−i300000000000000000000
χ4844-4-4400-4-4400000000-222-223−2323−23-2-22222-2-200000000000000000000110000-11-11-1-13−33−33−33−3000000000000
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χ5044-4-4400-4-4400000000-222-223−2323−231−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000000000000000000−1+i32−1−i3200001−i32−1+i321+i32−1−i321−i321+i32ζ3+2ζ15−ζ3−2ζ15ζ3+2ζ15−ζ3−2ζ15−2ζ3−ζ152ζ3+ζ15−2ζ3−ζ152ζ3+ζ15000000000000
χ5144-4-4400-4-4400000000-222-2−2323−2323-2-22222-2-200000000000000000000110000-11-11-1-1−33−33−33−33000000000000
χ5244-4-4400-4-4400000000-222-2−2323−23231+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000000000000000000−1−i32−1+i3200001+i32−1−i321−i32−1+i321+i321−i322ζ3+ζ15−2ζ3−ζ152ζ3+ζ15−2ζ3−ζ15−ζ3−2ζ15ζ3+2ζ15−ζ3−2ζ15ζ3+2ζ15000000000000
χ5344-4-4400-4-4400000000-222-2−2323−23231−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000000000000000000−1+i32−1−i3200001−i32−1+i321+i32−1−i321−i321+i32−ζ3−2ζ15ζ3+2ζ15−ζ3−2ζ15ζ3+2ζ152ζ3+ζ15−2ζ3−ζ152ζ3+ζ15−2ζ3−ζ15000000000000
χ544-44-44004-4-40000000044-4-40000-2-222-2-22200000000000000000000-2-200002222-2-200000000000000000000
χ554-44-44004-4-40000000044-4-400001+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i3000000000000000000001+i31−i30000−1−i3−1−i3−1+i3−1+i31+i31−i300000000000000000000
χ564-44-44004-4-40000000044-4-400001−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3000000000000000000001−i31+i30000−1+i3−1+i3−1−i3−1−i31−i31+i300000000000000000000
χ574-44-44004-4-400000000-2-222−2i32i32i3−2i3-2-222-2-22200000000000000000000110000-1-1-1-111−i3i3i3−i3−i3i3i3−i3000000000000
χ584-44-44004-4-400000000-2-222−2i32i32i3−2i31+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i300000000000000000000−1−i32−1+i3200001+i321+i321−i321−i32−1−i32−1+i32−3+i323−i323−i32−3+i323+i32−3−i32−3−i323+i32000000000000
χ594-44-44004-4-400000000-2-222−2i32i32i3−2i31−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i300000000000000000000−1+i32−1−i3200001−i321−i321+i321+i32−1+i32−1−i323+i32−3−i32−3−i323+i32−3+i323−i323−i32−3+i32000000000000
χ604-44-44004-4-400000000-2-2222i3−2i3−2i32i3-2-222-2-22200000000000000000000110000-1-1-1-111i3−i3−i3i3i3−i3−i3i3000000000000
χ614-44-44004-4-400000000-2-2222i3−2i3−2i32i31+i31−i3−1−i3−1+i31+i31−i3−1−i3−1+i300000000000000000000−1−i32−1+i3200001+i321+i321−i321−i32−1−i32−1+i323−i32−3+i32−3+i323−i32−3−i323+i323+i32−3−i32000000000000
χ624-44-44004-4-400000000-2-2222i3−2i3−2i32i31−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i300000000000000000000−1+i32−1−i3200001−i321−i321+i321+i32−1+i32−1−i32−3−i323+i323+i32−3−i323−i32−3+i32−3+i323−i32000000000000
χ6366666666666666-2-2-2-2-3-3-3-3-3-3-3-300000000-2-2-2-2111111111111000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 36 (ζ36 = 1); i = ζ9.