Paraphrasing the Summa: First part, Question 3, article 5

Article 5. Whether God is contained in a genus?

Is God one of a group?  In other words, is there more than one God?

Objection 1. It seems that God is contained in a genus. For a substance is a being that subsists of itself. But this is especially true of God. Therefore God is in a genus of substance.

God is a divine thing first and then God.  Therefore, God exists in a group.

Objection 2. Further, nothing can be measured save by something of its own genus; as length is measured by length and numbers by number. But God is the measure of all substances, as the Commentator shows (Metaph. x). Therefore God is in the genus of substance.

In addition, all things are comparable to other like things.  But God is not measured by any other thing.  Therefore, God is a type of divinity.

On the contrary, In the mind, genus is prior to what it contains. But nothing is prior to God either really or mentally. Therefore God is not in any genus.

St. Thomas says otherwise.  To the human mind, categories or groups precede individuals.  But God is before anything.  God is beyond any category or group which man can invent.

I answer that, A thing can be in a genus in two ways; either absolutely and properly, as a species contained under a genus; or as being reducible to it, as principles and privations. For example, a point and unity are reduced to the genus of quantity, as its principles; while blindness and all other privations are reduced to the genus of habit. But in neither way is God in a genus. That He cannot be a species of any genus may be shown in three ways.

There are two ways in which creatures can be grouped.  Either by a attributes they hold in common, such as human beings and monkeys, because of attributes they have in common, are specific beings under the the category of primate.  Or by attributes they don't hold, such as lacking the quality of sight, makes one blind, whether one is human or monkey.  Thus, there are sightless monkeys as well as sightless humans.

But in neither way is God in a genus. That He cannot be a species of any genus may be shown in three ways.

But God is in neither of those groups.  This can be proved in three ways.

First, because a species is constituted of genus and difference.

Kinds within a group are identified by their differences.

Now that from which the difference constituting the species is derived, is always related to that from which the genus is derived, as actuality is related to potentiality.

Within the group (genus), the various kinds (species) differ one from the other in the same degree as "that which is" to "that which could be".

*I know that "evolution" has a bad connotation to Christians, but, I get the impression that is what St. Thomas is talking about here.  Let's take the genus of primate.  All primates have hands, similar styled faces and exhibit similar behaviors.  So, to distinguish between them are the differences.  And these differences are almost evolutionary.  Monkeys have more unactualized potential than humans.  They are less evolved.

For animal is derived from sensitive nature, by concretion as it were, for that is animal, which has a sensitive nature.

Beasts are, by nature, sentient.  All beasts have the capacity to feel.

Rational being, on the other hand, is derived from intellectual nature, because that is rational, which has an intellectual nature,

Intelligent beings have intelligence.   Intelligent beings have the capacity to think logically.

and intelligence is compared to sense, as actuality is to potentiality.

And the capacity to think has the same relationship to the capacity to feel as reality has to possibility.

*Again, I see here a relationship of evolution.  Animals have the capacity to feel but have not evolved the capacity to think.

The same argument holds good in other things. Hence since in God actuality is not added to potentiality, it is impossible that He should be in any genus as a species.

But, God is different.  There is nothing and no one to whom He can be compared and everything is true to Him.  As the Scripture says, "Everything is possible with God" (Matt 19:26).

Secondly, since the existence of God is His essence, if God were in any genus, He would be the genus "being", because, since genus is predicated as an essential it refers to the essence of a thing. But the Philosopher has shown (Metaph. iii) that being cannot be a genus, for every genus has differences distinct from its generic essence. Now no difference can exist distinct from being; for non-being cannot be a difference. It follows then that God is not in a genus.

The second proof is this.  God's Divinity is His Reality, His Being.  If God were categorized, it would be as "Reality" because that is what He Is.  But, in order to categorize something, there must be a difference attributed to it within that category.  But since there is nothing and no one else which can be compared to God, then God can't be grouped or categorized.

Thirdly, because all in one genus agree in the quiddity or essence of the genus which is predicated of them as an essential, but they differ in their existence. For the existence of man and of horse is not the same; as also of this man and that man: thus in every member of a genus, existence and quiddity--i.e. essence--must differ. But in God they do not differ, as shown in the preceding article. Therefore it is plain that God is not in a genus as if He were a species. From this it is also plain that He has no genus nor difference, nor can there be any definition of Him; nor, save through His effects, a demonstration of Him: for a definition is from genus and difference; and the mean of a demonstration is a definition.

In a group or category, all share a certain nature within that group.  But, within that nature, they differ in real terms, they differ in being. Thus, a horse differs from a man, though they are both grouped with animals.

But, there is no other Being who can be grouped with God.  God is one and there is no other besides Him.

That God is not in a genus, as reducible to it as its principle, is clear from this, that a principle reducible to any genus does not extend beyond that genus; as, a point is the principle of continuous quantity alone; and unity, of discontinuous quantity. But God is the principle of all being. Therefore He is not contained in any genus as its principle.

God can not be categorized.  Because God is reality itself.  Therefore, all things exist in God and God can not be contained in one category.

Reply to Objection 1. The word substance signifies not only what exists of itself--for existence cannot of itself be a genus, as shown in the body of the article; but, it also signifies an essence that has the property of existing in this way--namely, of existing of itself; this existence, however, is not its essence. Thus it is clear that God is not in the genus of substance.

Reality is not a group.  Because that which is not "real" does not exist.  Therefore, reality is not a group.

On the other hand, the word "material" (i.e. substance) points not only to those things which are physically real, but also to those things which are made up of certain elements.  But there is a difference between their being and their nature.

In other words, gold is, by nature, hard.  But so is granite.

Reply to Objection 2. This objection turns upon proportionate measure which must be homogeneous with what is measured. Now, God is not a measure proportionate to anything. Still, He is called the measure of all things, in the sense that everything has being only according as it resembles Him.

God is the measure of all things but God Himself can not be measured.  Therefore, man can not conceive the magnitude of God's Being.  And can not, therefore, put God in any category or group.  God is beyond man's ability to comprehend.