Finite Group Databasebeta

← Group #7407

Character table — Group #7407

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31
size1111224444448888888888161616161616161616
order124424248888241616161616161616248888888
χ11111111111111111111111111111111
χ21111111111111111111111-1-11-1-1-1-1-1-1
χ311111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ411111111111111-1-1-1-1-1-1-1-1-1-11-1-11111
χ511111111-1-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−i
χ611111111-1-1-1-1-1-1iiii−i−i−i−i-1-1111−i−iii
χ711111111-1-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii
χ811111111-1-1-1-1-1-1−i−i−i−iiiii-1-1111ii−i−i
χ9222222222222-2-20000000000-2000000
χ1022222222-2-2-2-2220000000000-2000000
χ1122-2-22-22-22i2i−2i−2i0000000000000001+i−1−i1−i−1+i
χ1222-2-22-22-22i2i−2i−2i000000000000000−1−i1+i−1+i1−i
χ1322-2-22-22-2−2i−2i2i2i0000000000000001−i−1+i1+i−1−i
χ1422-2-22-22-2−2i−2i2i2i000000000000000−1+i1−i−1−i1+i
χ1522-2-22-2-2200002-2i2i2−i2−i2i2i2−i2−i2000000000
χ1622-2-22-2-2200002-2−i2−i2i2i2−i2−i2i2i2000000000
χ1722-2-22-2-220000-2222−2−2−2−222000000000
χ1822-2-22-2-220000-22−2−22222−2−2000000000
χ19444444-4-400000000000000000000000
χ204444-4-400000000000000000002-20000
χ214444-4-40000000000000000000-220000
χ2244-4-4-4400000000000000002-20000000
χ2344-4-4-440000000000000000-220000000
χ244-44i−4i00002ζ2−2ζ22ζ6−2ζ600ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7000000000
χ254-44i−4i00002ζ2−2ζ22ζ6−2ζ600−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7000000000
χ264-44i−4i0000−2ζ22ζ2−2ζ62ζ600ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7000000000
χ274-44i−4i0000−2ζ22ζ2−2ζ62ζ600−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7000000000
χ284-4−4i4i00002ζ6−2ζ62ζ2−2ζ200ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5000000000
χ294-4−4i4i00002ζ6−2ζ62ζ2−2ζ200−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5000000000
χ304-4−4i4i0000−2ζ62ζ6−2ζ22ζ200ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5000000000
χ314-4−4i4i0000−2ζ62ζ6−2ζ22ζ200−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.