Finite Group Databasebeta

← Group #3666

Character table — Group #3666

Order 144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size111122222222222222229999111122222222222222229999
order1244369991212181818363636363636888822446618181812121818183636363636368888
χ1111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-111111111111111111111-1-1-1-1
χ311-1-111111-1-1111-1-1-1-1-1-1ii−i−i11-1-111111-1-1111-1-1-1-1-1-1ii−i−i
χ411-1-111111-1-1111-1-1-1-1-1-1−i−iii11-1-111111-1-1111-1-1-1-1-1-1−i−iii
χ51-1i−i1-1111i−i-1-1-1iii−i−i−iζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ391-1i−i1-1111i−i-1-1-1iii−i−i−iζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ61-1i−i1-1111i−i-1-1-1iii−i−i−i−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ391-1i−i1-1111i−i-1-1-1iii−i−i−i−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39
χ71-1−ii1-1111−ii-1-1-1−i−i−iiii−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ691-1−ii1-1111−ii-1-1-1−i−i−iiii−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69
χ81-1−ii1-1111−ii-1-1-1−i−i−iiiiζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ691-1−ii1-1111−ii-1-1-1−i−i−iiiiζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69
χ9222222-1-1-122-1-1-1-1-1-1-1-1-10000222222-1-1-122-1-1-1-1-1-1-1-1-10000
χ102222-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6800002222-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000
χ112222-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ6800002222-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000
χ122222-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ5200002222-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000
χ1322-2-222-1-1-1-2-2-1-1-1111111000022-2-222-1-1-1-2-2-1-1-11111110000
χ1422-2-2-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6811ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68000022-2-2-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6811ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ680000
χ1522-2-2-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ6811ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68000022-2-2-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ6811ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ680000
χ1622-2-2-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ5211−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52000022-2-2-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ5211−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ520000
χ172-22i−2i2-2-1-1-12i−2i111−i−i−iiii00002-22i−2i2-2-1-1-12i−2i111−i−i−iiii0000
χ182-22i−2i-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ii−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ2200002-22i−2i-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ii−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ220000
χ192-22i−2i-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ii−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ70−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ7000002-22i−2i-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ii−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ70−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ700000
χ202-22i−2i-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−iiζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ7000002-22i−2i-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−iiζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ700000
χ212-2−2i2i2-2-1-1-1−2i2i111iii−i−i−i00002-2−2i2i2-2-1-1-1−2i2i111iii−i−i−i0000
χ222-2−2i2i-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68i−i−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ2200002-2−2i2i-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68i−i−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ220000
χ232-2−2i2i-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68i−i−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ70ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ7000002-2−2i2i-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68i−i−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ70ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ700000
χ242-2−2i2i-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52i−iζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ7000002-2−2i2i-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52i−iζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ700000
χ25111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ2611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ2711-1-111111-1-1111-1-1-1-1-1-1ii−i−i-1-111-1-1-1-1-111-1-1-1111111−i−iii
χ2811-1-111111-1-1111-1-1-1-1-1-1−i−iii-1-111-1-1-1-1-111-1-1-1111111ii−i−i
χ291-1i−i1-1111i−i-1-1-1iii−i−i−iζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39-11−ii-11-1-1-1−ii111−i−i−iiii−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39
χ301-1i−i1-1111i−i-1-1-1iii−i−i−i−ζ21−ζ69ζ21+ζ69ζ15+ζ39−ζ15−ζ39-11−ii-11-1-1-1−ii111−i−i−iiiiζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ311-1−ii1-1111−ii-1-1-1−i−i−iiii−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69-11i−i-11-1-1-1i−i111iii−i−i−iζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69
χ321-1−ii1-1111−ii-1-1-1−i−i−iiiiζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69-11i−i-11-1-1-1i−i111iii−i−i−i−ζ15−ζ39ζ15+ζ39ζ21+ζ69−ζ21−ζ69
χ33222222-1-1-122-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-2111-2-21111111110000
χ342222-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000-2-2-2-211−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ6811−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ680000
χ352222-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000-2-2-2-211−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ6811−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ680000
χ362222-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000-2-2-2-211ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ5211ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ520000
χ3722-2-222-1-1-1-2-2-1-1-11111110000-2-222-2-211122111-1-1-1-1-1-10000
χ3822-2-2-1-1ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ6811ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ680000-2-22211−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68-1-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ680000
χ3922-2-2-1-1ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ6811ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ680000-2-22211−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68-1-1−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ680000
χ4022-2-2-1-1−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ5211−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ520000-2-22211ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52-1-1ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ520000
χ412-22i−2i2-2-1-1-12i−2i111−i−i−iiii0000-22−2i2i-22111−2i2i-1-1-1iii−i−i−i0000
χ422-22i−2i-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ii−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ220000-22−2i2i1-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68i−iζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ220000
χ432-22i−2i-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ii−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ70−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ700000-22−2i2i1-1−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68i−iζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ70ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ700000
χ442-22i−2i-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−iiζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ700000-22−2i2i1-1ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52i−i−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ700000
χ452-2−2i2i2-2-1-1-1−2i2i111iii−i−i−i0000-222i−2i-221112i−2i-1-1-1−i−i−iiii0000
χ462-2−2i2i-11ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68i−i−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ220000-222i−2i1-1−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ4+ζ68−iiζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ4−ζ68ζ14+ζ62−ζ70ζ22−ζ62+ζ70−ζ14−ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70ζ14+ζ220000
χ472-2−2i2i-11ζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68i−i−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ70ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ700000-222i−2i1-1−ζ4+ζ44−ζ52ζ4+ζ68−ζ44+ζ52−ζ68−iiζ4−ζ44+ζ52−ζ4−ζ68ζ44−ζ52+ζ68ζ22−ζ62+ζ70−ζ14−ζ22ζ14+ζ62−ζ70−ζ22+ζ62−ζ70ζ14+ζ22−ζ14−ζ62+ζ700000
χ482-2−2i2i-11−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52i−iζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ70−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ700000-222i−2i1-1ζ4+ζ68−ζ44+ζ52−ζ68−ζ4+ζ44−ζ52−ii−ζ4−ζ68ζ44−ζ52+ζ68ζ4−ζ44+ζ52−ζ14−ζ22ζ14+ζ62−ζ70ζ22−ζ62+ζ70ζ14+ζ22−ζ14−ζ62+ζ70−ζ22+ζ62−ζ700000

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