Finite Group Databasebeta

← Group #10619503

Character table — Group #10619503

Order 648.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122226666666666666666999999991818181818181818272727272727272727272727
order12443612123699912121818183636363636363366121212129918183636363688882424242424242424
χ11111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111−1−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
χ4111111111111111111111111−1−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
χ5111111111111111111111111−1+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
χ6111111111111111111111111−1+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
χ711-1-111-1-111111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−i
χ811-1-111-1-111111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii
χ911-1-111-1-111111-1-1111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32ii−i−i−ζ30−ζ30ζ30ζ30−ζ6−ζ6ζ6ζ6
χ1011-1-111-1-111111-1-1111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−i−iiiζ30ζ30−ζ30−ζ30ζ6ζ6−ζ6−ζ6
χ1111-1-111-1-111111-1-1111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32ii−i−i−ζ6−ζ6ζ6ζ6−ζ30−ζ30ζ30ζ30
χ1211-1-111-1-111111-1-1111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−i−iiiζ6ζ6−ζ6−ζ6ζ30ζ30−ζ30−ζ30
χ131-1i−i1-1i−i1-1111i−i-1-1-1iii−i−i−i11-1-1i−ii−i11-1-1i−ii−iζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ141-1i−i1-1i−i1-1111i−i-1-1-1iii−i−i−i11-1-1i−ii−i11-1-1i−ii−i−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39
χ151-1i−i1-1i−i1-1111i−i-1-1-1iii−i−i−i−1−i32−1+i321+i321−i32−ζ30ζ30−ζ6ζ6−1−i32−1+i321+i321−i32−ζ30ζ30−ζ6ζ6ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ21ζ21ζ39−ζ39−ζ69ζ69ζ15−ζ15
χ161-1i−i1-1i−i1-1111i−i-1-1-1iii−i−i−i−1−i32−1+i321+i321−i32−ζ30ζ30−ζ6ζ6−1−i32−1+i321+i321−i32−ζ30ζ30−ζ6ζ6−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ21−ζ21−ζ39ζ39ζ69−ζ69−ζ15ζ15
χ171-1i−i1-1i−i1-1111i−i-1-1-1iii−i−i−i−1+i32−1−i321−i321+i32−ζ6ζ6−ζ30ζ30−1+i32−1−i321−i321+i32−ζ6ζ6−ζ30ζ30ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39−ζ69ζ69ζ15−ζ15−ζ21ζ21ζ39−ζ39
χ181-1i−i1-1i−i1-1111i−i-1-1-1iii−i−i−i−1+i32−1−i321−i321+i32−ζ6ζ6−ζ30ζ30−1+i32−1−i321−i321+i32−ζ6ζ6−ζ30ζ30−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39ζ69−ζ69−ζ15ζ15ζ21−ζ21−ζ39ζ39
χ191-1−ii1-1−ii1-1111−ii-1-1-1−i−i−iiii11-1-1−ii−ii11-1-1−ii−ii−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69
χ201-1−ii1-1−ii1-1111−ii-1-1-1−i−i−iiii11-1-1−ii−ii11-1-1−ii−iiζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69
χ211-1−ii1-1−ii1-1111−ii-1-1-1−i−i−iiii−1−i32−1+i321+i321−i32ζ30−ζ30ζ6−ζ6−1−i32−1+i321+i321−i32ζ30−ζ30ζ6−ζ6−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69ζ39−ζ39−ζ21ζ21ζ15−ζ15−ζ69ζ69
χ221-1−ii1-1−ii1-1111−ii-1-1-1−i−i−iiii−1−i32−1+i321+i321−i32ζ30−ζ30ζ6−ζ6−1−i32−1+i321+i321−i32ζ30−ζ30ζ6−ζ6ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69−ζ39ζ39ζ21−ζ21−ζ15ζ15ζ69−ζ69
χ231-1−ii1-1−ii1-1111−ii-1-1-1−i−i−iiii−1+i32−1−i321−i321+i32ζ6−ζ6ζ30−ζ30−1+i32−1−i321−i321+i32ζ6−ζ6ζ30−ζ30−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69ζ15−ζ15−ζ69ζ69ζ39−ζ39−ζ21ζ21
χ241-1−ii1-1−ii1-1111−ii-1-1-1−i−i−iiii−1+i32−1−i321−i321+i32ζ6−ζ6ζ30−ζ30−1+i32−1−i321−i321+i32ζ6−ζ6ζ30−ζ30ζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69−ζ15ζ15ζ69−ζ69−ζ39ζ39ζ21−ζ21
χ252222222222-1-1-122-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1000000000000
χ262222222222-1-1-122-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i321−i321+i321−i321+i321+i321−i321−i32000000000000
χ272222222222-1-1-122-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i321+i321−i321+i321−i321−i321+i321+i32000000000000
χ2822-2-222-2-222-1-1-1-2-2-1-1-11111112222-2-2-2-2-1-1-1-11111000000000000
χ2922-2-222-2-222-1-1-1-2-2-1-1-1111111−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32000000000000
χ3022-2-222-2-222-1-1-1-2-2-1-1-1111111−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i31−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32000000000000
χ312-22i−2i2-22i−2i2-2-1-1-12i−2i111−i−i−iiii22-2-22i−2i2i−2i-1-111−ii−ii000000000000
χ322-22i−2i2-22i−2i2-2-1-1-12i−2i111−i−i−iiii−1−i3−1+i31+i31−i3−2ζ302ζ30−2ζ62ζ61+i321−i32−1−i32−1+i32ζ30−ζ30ζ6−ζ6000000000000
χ332-22i−2i2-22i−2i2-2-1-1-12i−2i111−i−i−iiii−1+i3−1−i31−i31+i3−2ζ62ζ6−2ζ302ζ301−i321+i32−1+i32−1−i32ζ6−ζ6ζ30−ζ30000000000000
χ342-2−2i2i2-2−2i2i2-2-1-1-1−2i2i111iii−i−i−i22-2-2−2i2i−2i2i-1-111i−ii−i000000000000
χ352-2−2i2i2-2−2i2i2-2-1-1-1−2i2i111iii−i−i−i−1−i3−1+i31+i31−i32ζ30−2ζ302ζ6−2ζ61+i321−i32−1−i32−1+i32−ζ30ζ30−ζ6ζ6000000000000
χ362-2−2i2i2-2−2i2i2-2-1-1-1−2i2i111iii−i−i−i−1+i3−1−i31−i31+i32ζ6−2ζ62ζ30−2ζ301−i321+i32−1+i32−1−i32−ζ6ζ6−ζ30ζ30000000000000
χ3766666666-3-3000-3-30000000000000000000000000000000000000
χ386666-3-3-3-300ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ680000000000000000000000000000
χ396666-3-3-3-300ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ680000000000000000000000000000
χ406666-3-3-3-300−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ680000000000000000000000000000
χ4166-6-666-6-6-3-3000330000000000000000000000000000000000000
χ4266-6-6-3-33300ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ680000000000000000000000000000
χ4366-6-6-3-33300ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ680000000000000000000000000000
χ4466-6-6-3-33300−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ6800−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ680000000000000000000000000000
χ456-66i−6i6-66i−6i-33000−3i3i0000000000000000000000000000000000000
χ466-66i−6i-33−3i3i00ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ682ζ14+ζ22+ζ62−ζ70−ζ14+ζ22−2ζ62+2ζ70−ζ14−2ζ22+ζ62−ζ70−2ζ14−ζ22−ζ62+ζ70ζ14−ζ22+2ζ62−2ζ70ζ14+2ζ22−ζ62+ζ700000000000000000000000000000
χ476-66i−6i-33−3i3i00ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ14+ζ22−2ζ62+2ζ70−ζ14−2ζ22+ζ62−ζ702ζ14+ζ22+ζ62−ζ70ζ14−ζ22+2ζ62−2ζ70ζ14+2ζ22−ζ62+ζ70−2ζ14−ζ22−ζ62+ζ700000000000000000000000000000
χ486-66i−6i-33−3i3i00−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68002ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ68−ζ14−2ζ22+ζ62−ζ702ζ14+ζ22+ζ62−ζ70−ζ14+ζ22−2ζ62+2ζ70ζ14+2ζ22−ζ62+ζ70−2ζ14−ζ22−ζ62+ζ70ζ14−ζ22+2ζ62−2ζ700000000000000000000000000000
χ496-6−6i6i6-6−6i6i-330003i−3i0000000000000000000000000000000000000
χ506-6−6i6i-333i−3i00ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ6800−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−2ζ14−ζ22−ζ62+ζ70ζ14−ζ22+2ζ62−2ζ70ζ14+2ζ22−ζ62+ζ702ζ14+ζ22+ζ62−ζ70−ζ14+ζ22−2ζ62+2ζ70−ζ14−2ζ22+ζ62−ζ700000000000000000000000000000
χ516-6−6i6i-333i−3i00ζ4−2ζ44+2ζ52−ζ68−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ6800−ζ4+2ζ44−2ζ52+ζ682ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68ζ14−ζ22+2ζ62−2ζ70ζ14+2ζ22−ζ62+ζ70−2ζ14−ζ22−ζ62+ζ70−ζ14+ζ22−2ζ62+2ζ70−ζ14−2ζ22+ζ62−ζ702ζ14+ζ22+ζ62−ζ700000000000000000000000000000
χ526-6−6i6i-333i−3i00−2ζ4+ζ44−ζ52−ζ68ζ4+ζ44−ζ52+2ζ68ζ4−2ζ44+2ζ52−ζ68002ζ4−ζ44+ζ52+ζ68−ζ4−ζ44+ζ52−2ζ68−ζ4+2ζ44−2ζ52+ζ68ζ14+2ζ22−ζ62+ζ70−2ζ14−ζ22−ζ62+ζ70ζ14−ζ22+2ζ62−2ζ70−ζ14−2ζ22+ζ62−ζ702ζ14+ζ22+ζ62−ζ70−ζ14+ζ22−2ζ62+2ζ700000000000000000000000000000

Here ζ is a primitive root of unity of order 72 (ζ72 = 1); i = ζ18.