Finite Group Databasebeta

← Group #68013

Character table — Group #68013

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24
size133333466666666121212121264646464
order124444288888888488883366
χ1111111111111111111111111
χ211111111111111111111−1−i32−1+i32−1−i32−1+i32
χ311111111111111111111−1+i32−1−i32−1+i32−1−i32
χ4111111-111111111-1-1-1-1-111-1-1
χ5111111-111111111-1-1-1-1-1−1−i32−1+i321+i321−i32
χ6111111-111111111-1-1-1-1-1−1+i32−1−i321−i321+i32
χ73333333-1-1-1-1-1-1-1-13-1-1-1-10000
χ8333333-3-1-1-1-1-1-1-1-1-311110000
χ933-1-1-1-131111−1+2i−1+2i−1−2i−1−2i-111−1+2i−1−2i0000
χ1033-1-1-1-131111−1−2i−1−2i−1+2i−1+2i-111−1−2i−1+2i0000
χ1133-1-1-1-13−1+2i−1+2i−1−2i−1−2i1111-1−1+2i−1−2i110000
χ1233-1-1-1-13−1−2i−1−2i−1+2i−1+2i1111-1−1−2i−1+2i110000
χ1333-1-1-1-1-31111−1+2i−1+2i−1−2i−1−2i1-1-11−2i1+2i0000
χ1433-1-1-1-1-31111−1−2i−1−2i−1+2i−1+2i1-1-11+2i1−2i0000
χ1533-1-1-1-1-3−1+2i−1+2i−1−2i−1−2i111111−2i1+2i-1-10000
χ1633-1-1-1-1-3−1−2i−1−2i−1+2i−1+2i111111+2i1−2i-1-10000
χ176-222−2+4i−2−4i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000
χ186-222−2+4i−2−4i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000
χ196-222−2−4i−2+4i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000
χ206-222−2−4i−2+4i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000
χ216-2−2+4i−2−4i2202ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000
χ226-2−2+4i−2−4i220−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000
χ236-2−2−4i−2+4i220−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000
χ246-2−2−4i−2+4i2202ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.