Finite Group Databasebeta

← Group #604

Character table — Group #604

Order 72.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24
size111122222222222222229999
order12443699912121818183636363636368888
χ1111111111111111111111111
χ211111111111111111111-1-1-1-1
χ311-1-111111-1-1111-1-1-1-1-1-1ii−i−i
χ411-1-111111-1-1111-1-1-1-1-1-1−i−iii
χ51-1i−i1-1111i−i-1-1-1iii−i−i−iζ21+ζ69−ζ21−ζ69−ζ15−ζ39ζ15+ζ39
χ61-1i−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−ζ69
χ81-1−ii1-1111−ii-1-1-1−i−i−iiiiζ15+ζ39−ζ15−ζ39−ζ21−ζ69ζ21+ζ69
χ9222222-1-1-122-1-1-1-1-1-1-1-1-10000
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−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+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+ζ520000
χ1322-2-222-1-1-1-2-2-1-1-11111110000
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+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−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−ζ520000
χ172-22i−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+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+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−ζ700000
χ212-2−2i2i2-2-1-1-1−2i2i111iii−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−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−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+ζ700000

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