C Eb and Gb is a diminished fifth.
If you add A, it is a diminished seventh.
There is no chord consisting of C E and Ab.
If you see such a thing, the Ab is a non-harmonic tone, and I betcha the Ab resolves to a G.
I know one way to learn the chords,
but it will require a small arts and crafts project.
You need:
several sheets of cardboard or poster board
a pencil
a felt marker
a compass
a ruler
a protractor
a copper pin fastener
a pair of scissors.
1. With the compass, draw a circle on one sheet of cardboard or posterboard.
2. With the protractor and pencil, divide that circle into 12 slices of 30 degrees each.
3. With the scissors, cut the circle out.
4. With the felt marker, label those slices on the edge as C, G, d, A, E, B, F#, C#, Ab, Eb, Bb, F.
You have now finished making the Circle of Fifths.
5. Cut out another circle the same size as the Circle of Fifths.
Cut out peepholes for C, G, and E.
Draw an arrow pointing to the C.
With the felt marker, label this as "major."
6. Flip the major wheel over and try laying it on the Circle of Fifths.
You should be able to adjust it so that you see C, G, and Eb.
On this side also, draw an arrow pointing to the C.
Label this side "minor."
7. Make another wheel like the major wheel, only this time, cut another peephole for the Bb.
Again, draw an arrow pointing to the C.
Label this one "seventh."
8. For "diminished seventh," cut out peepholes for C, Eb, F#, and A, but don't draw any arrows.
This same chord can go all four ways.
9. For "augmented," the peepholes are at C, E, G#.
This chord can go all three ways.
To find a major chord, put the major wheel on top of the Circle of Fiths, fasten in the center with the copper pin, and rotate.
Whatever the arrow is pointing to is the name of the major chord.
The same procedure serves for all the other chords.
For major sevenths (or major-major), the peepholes are at C, E, G, and B.
For minor sevenths (or minor-minor), the peepholes are at C, Eb, G, and Bb.
For dominant sevenths (or major-minor), the peepholes are at C, E, G, and Bb.
For French sixths, the peepholes are at Ab, C, D, and F#.
For Italian sixths, the peepholes are at Ab, C, and F#.
For German sixths, you can use the wheel for sevenths.
For half diminished sevenths (or the Tristan chord), the peepholes are B, F, D, and A.