Finite Group Databasebeta

← Group #4628

Character table — Group #4628

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32
size111111116666666666668888888812121212
order12448888248816161616161616163612122424242416161616
χ111111111111111111111111111111111
χ2111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ31111-1-1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1ii−i−i
χ41111-1-1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−iii
χ511-1-1ii−i−i-11i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ611-1-1ii−i−iζ2−ζ2ζ6−ζ6
χ611-1-1ii−i−i-11i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ611-1-1ii−i−i−ζ2ζ2−ζ6ζ6
χ711-1-1−i−iii-11−iiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ211-1-1−i−iiiζ6−ζ6ζ2−ζ2
χ811-1-1−i−iii-11−ii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ211-1-1−i−iii−ζ6ζ6−ζ2ζ2
χ922222222222200000000-1-1-1-1-1-1-1-10000
χ102222-2-2-2-222-2-200000000-1-1-1-111110000
χ1122-2-22i2i−2i−2i-222i−2i00000000-1-111−i−iii0000
χ1222-2-2−2i−2i2i2i-22−2i2i00000000-1-111ii−i−i0000
χ132-22i−2i2ζ2−2ζ22ζ6−2ζ60000ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5-11i−iζ2−ζ2ζ6−ζ60000
χ142-22i−2i2ζ2−2ζ22ζ6−2ζ60000−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5-11i−iζ2−ζ2ζ6−ζ60000
χ152-22i−2i−2ζ22ζ2−2ζ62ζ60000ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5-11i−i−ζ2ζ2−ζ6ζ60000
χ162-22i−2i−2ζ22ζ2−2ζ62ζ60000−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5-11i−i−ζ2ζ2−ζ6ζ60000
χ172-2−2i2i2ζ6−2ζ62ζ2−2ζ20000ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7-11−iiζ6−ζ6ζ2−ζ20000
χ182-2−2i2i2ζ6−2ζ62ζ2−2ζ20000−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7-11−iiζ6−ζ6ζ2−ζ20000
χ192-2−2i2i−2ζ62ζ6−2ζ22ζ20000ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7-11−ii−ζ6ζ6−ζ2ζ20000
χ202-2−2i2i−2ζ62ζ6−2ζ22ζ20000−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7-11−ii−ζ6ζ6−ζ2ζ20000
χ2133333333-1-1-1-11111111100000000-1-1-1-1
χ2233333333-1-1-1-1-1-1-1-1-1-1-1-1000000001111
χ233333-3-3-3-3-1-111iiii−i−i−i−i00000000−i−iii
χ243333-3-3-3-3-1-111−i−i−i−iiiii00000000ii−i−i
χ2533-3-33i3i−3i−3i1-1−iiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ600000000−ζ2ζ2−ζ6ζ6
χ2633-3-33i3i−3i−3i1-1−ii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ600000000ζ2−ζ2ζ6−ζ6
χ2733-3-3−3i−3i3i3i1-1i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ200000000−ζ6ζ6−ζ2ζ2
χ2833-3-3−3i−3i3i3i1-1i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ200000000ζ6−ζ6ζ2−ζ2
χ294-44i−4i4ζ2−4ζ24ζ6−4ζ60000000000001-1−ii−ζ2ζ2−ζ6ζ60000
χ304-44i−4i−4ζ24ζ2−4ζ64ζ60000000000001-1−iiζ2−ζ2ζ6−ζ60000
χ314-4−4i4i4ζ6−4ζ64ζ2−4ζ20000000000001-1i−i−ζ6ζ6−ζ2ζ20000
χ324-4−4i4i−4ζ64ζ6−4ζ24ζ20000000000001-1i−iζ6−ζ6ζ2−ζ20000

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