Pension Credit

Meant to say Age UK has a good website.

£168 is for s single person, obvs.

It's supposed to make up your income to the SRP rate of £168.

If she has gaps in her contributions and no other form of income )such as an occupational pension or private pension) then she could be entitled.

She could also be entitled to other underlying entitlements such as free dental care.

Entitled To is the best calculator to use imho.

I'd assume that would be the total amount including state pension.

I presume you mean that you have done an online calculation, which asks about all forms of income, (including state pension) and savings?
If she lives alone and gets a state pension, I am struggling to see how she could be entitled to anywhere near as much as £145 a week, unless that state pension is tiny.

This is what the MSE website says:

Guarantee credit

For single pensioners with a weekly income (including pension) below £167.25, pension credit will top you up to £167.25.

When you apply for guarantee credit, the Government looks at all of your income. This includes both your basic and additional state pension, any income from other pensions, income from any jobs or social security benefits you have, and any savings and investments above £10,000.

You'll have to get in touch with your local DWP .