Identify the kind of molecular symmetry being tested

The options ask whether the given compound has:

• optical activity,
• centre of symmetry,
• plane of symmetry,
• axis of symmetry.

For such questions, the key idea is:

• If a molecule has a plane of symmetry or centre of symmetry, it is generally achiral and hence optically inactive.
• A molecule can still be optically active even if it has a proper rotational axis $C_n$.

Use the stored structure-based conclusion

From the given compound, the relevant symmetry elements are:

• it is chiral, so it is optically active;
• it has a rotational axis of symmetry;
• it does not have a plane of symmetry;
• it does not have a centre of symmetry.

Evaluate each option

A: The compound is optically active.
Since the molecule is chiral, this is correct.

B: The compound possesses centre of symmetry.
A centre of symmetry would make the molecule achiral here, so this is incorrect.

C: The compound possesses plane of symmetry.
A plane of symmetry would also destroy chirality, so this is incorrect.

D: The compound possesses axis of symmetry.
The compound does have a proper rotational axis, so this is correct.

Final answer

The correct statements are: $\boxed{A,\ D}$

Comparison with stored correct answer

Stored correct answer: $A, D$
Derived answer: $A, D$

Hence, the derived answer agrees with the stored correct answer.