This is exactly what I was going to point out.
Dilithium is an element (ot a compound) in the Star Trek universe, Dt, atomic number 87.
Recite? Yeah, right. I had to take Chem 101 and 102 back in '76/77. I passed. I know the periodic table has lots of letters and colors and numbers - I even know what some of them mean. But chemistry is magic and I don’t believe in magic.
Who knew there was divisiveness on the periodic table?
Hydrogen, Helium, … …
Actually, there really is. Although it’s usually cited as a brilliant accomplishment that helps us understand the atomic structure of the elements, I tend to side with those who see it as an asymmetrical oddball mess, for example with the lanthanides and actinides not fitting into the table at all, but having to be separated out into their own rows. But this is not a serious objection and comes from someone who is not a chemist, so chemists will kindly give me a break and leave me alone. 
Same here. But 40 years ago……
My brother has his BS in Chemistry with a Statistics minor, IIRC. I asked him the OP’s question once, years ago. He took a piece of paper and began drawing a periodic table, along with why it is the way it is. He completed the entire thing.
Oddly, he only used his statistics degree in his career (he is retired).
I am most definitely not a chemist or even chemist wannabe. Most of my topic knowledge comes from memorizing Tom Lehrer’s song when I was a teen.
But the lanthanides and actinides totally DO fit into the table. The table as it really is very wide and not real tall. And so fits badly on the usual standard shapes for books and paper. So as a page layout convention those two sections are usually cut out of the middle of the actual table and printed down below, letting the interior edges of the left and right margins of the real table snug together wrongfully in the space where the two moved rows actually belong. The table we’re all used to seeing has been butchered to fit on the paper.
This is no different than a 50-state US map showing both Hawaii & Alaska as insets just off the coast of California.
See this section of this article. Best viewed on a real PC with a real landscape format screen, not on a phone.
This shows a series of graphics growing the table step by step from holding just Hydrogen and Helium in the top-most row to including all the elements in all the rows and with all the columns shown in their correct places. The shape of the table makes a lot more sense once you see how it builds up. And once you see it on a wide screen as a single unit, not something chopped into chunks to fit neatly on old-fashioned paper.
As a metaphor, when I was a little kid I didn’t understand why Alaska was full of polar bears and glaciers while Hawaii was full of palm trees and warm water when they’re right next to each other and also right next to California where I lived with warm-ish air and a cool/cold ocean. Bad page design decisions can inadvertently really screw with user understanding.
As to why that particular asymmetrical overall shape …
One of the problems of science is that we’re stuck with how the universe is designed. We just get to describe it, not improve it. Since electron orbital behavior was designed asymmetrically, we’re kinda stuck with an asymmetrical table to describe it.
Well, that only applies to the Mendeleev format of the Periodic Table. There are alternative formats (see Wikipedia), mostly circular with projecting spokes for the lanthanides and actinides. And even the Mendeleevian version has changed, as better info is learned. Like the atomic weight of Carbon has changed from 12 to the more accurate 12.0096 .
But really, what is the point in memorizing the Periodic Table? Why occupy your brain with such trivia?
The value of the Periodic Table is the visual way it reflects the orderly makeup of the elements, how elements in columns show similar physical properties, and how those properties are connected to the composition of the atoms. It’s a big picture item, and when a scientist needs the specific details on an element, they properly look it up, rather than rely on their memory of the Periodic Table.
What always bugs me is when someone tries to make a “Periodic Table of <something else>”. The Periodic Table is arranged the way it is because it shows real patterns that exist in the elements. Arrange the elements, in order, with this many per row (increasing appropriately in lower rows), and you end up with all of the elements in the same column having similar properties, and trends in various properties as you move through the table (more electronegative to the right, etc.). When you make a “periodic table of junk food”, or “periodic table of Minecraft blocks”, or whatever, that doesn’t happen. Often, there isn’t even any logical analogue to “atomic number”, to begin with.
umm to impress women?
Well, sure, but the intersection of the groups (the vertical columns, which AIUI denote the number of valence electrons – except when they don’t – which is enough to make my non-chemist’s head hurt) and the rows (periods) generally contains a single element, except for Group 3 Period 6 and Period 7, where the 15 lanthanides and 15 actinides reside (see below). Again, I’m not being completely serious here, but the periodic table is most certainly not a straightforward, symmetrical rectangle – because as you say, the universe isn’t built that way. Leave me alone, I have a right to be grouchy about it!
That’s certainly why I do it.
Once again, AIUI this is simply factually wrong. You’re apparently conflating how the graphic is drawn with how the underlying table and underlying reality is structured.
The last graphic in the wiki section I cited has it correct. Group 3 period 6 is Lutecium (Lu) and only Lutecium. The other 13 lanthanides live between Groups 2 and 3. similarly Group 3 period 7 is Lawrencium (Lr) and only Lawrencium. The other 13 actinides live between Groups 2 and 3.
And yes, you’re fully entitled to your peeves. I just wish Nature had designed human’s internal plumbing more logically and redundantly. Humans have way too few back-up systems. Grr!
Yes, thanks, I can see now that the Wiki article specifically says that “The f-block groups are ignored in this [group] numbering” and that “For reasons of space, the periodic table is commonly presented with the f-block elements cut out and positioned as a distinct part below the main body”. The f-block being the lanthanides and actinides. So presenting them as being in Group 3 is a fiction.
In summary: the periodic table is even more messed up than I had thought! 
Count me in with those who can fill in far more than what we can recite. I think of it in periods. So I can only say it in order without thinking “what’s above it?” through Zr.
I never bothered learning the f-block or the last row of the d- and p- blocks.
Which is wrong. Periods = rows. I think of it in groups/columns.
Much less than I could decades ago.
Our class wasn’t required to memorize the periodic table. A large one hung at the front of the room near the blackboard.
We did have to learn the Noble Gases.
I never memorized them directly, either. Just tried it, and got the first four, but forgot about boron. And I barely remembered beryllium.