Here's the output of the GAP command "SmallGroupsInformation(512)" > There are 10494213 groups of order 512. > 1 is cyclic. > 2 - 10 have rank 2 and p-class 3. > 11 - 386 have rank 2 and p-class 4. > 387 - 1698 have rank 2 and p-class 5. > 1699 - 2008 have rank 2 and p-class 6. > 2009 - 2039 have rank 2 and p-class 7. > 2040 - 2044 have rank 2 and p-class 8. > 2045 has rank 3 and p-class 2. > 2046 - 29398 have rank 3 and p-class 3. > 29399 - 30617 have rank 3 and p-class 4. > 30618 - 31239 have rank 3 and p-class 3. > 31240 - 56685 have rank 3 and p-class 4. > 56686 - 60615 have rank 3 and p-class 5. > 60616 - 60894 have rank 3 and p-class 6. > 60895 - 60903 have rank 3 and p-class 7. > 60904 - 67612 have rank 4 and p-class 2. > 67613 - 387088 have rank 4 and p-class 3. > 387089 - 419734 have rank 4 and p-class 4. > 419735 - 420500 have rank 4 and p-class 5. > 420501 - 420514 have rank 4 and p-class 6. > 420515 - 6249623 have rank 5 and p-class 2. > 6249624 - 7529606 have rank 5 and p-class 3. > 7529607 - 7532374 have rank 5 and p-class 4. > 7532375 - 7532392 have rank 5 and p-class 5. > 7532393 - 10481221 have rank 6 and p-class 2. > 10481222 - 10493038 have rank 6 and p-class 3. > 10493039 - 10493061 have rank 6 and p-class 4. > 10493062 - 10494173 have rank 7 and p-class 2. > 10494174 - 10494200 have rank 7 and p-class 3. > 10494201 - 10494212 have rank 8 and p-class 2. > 10494213 is elementary abelian. > This size belongs to layer 7 of the SmallGroups library. > IdSmallGroup is not available for this size. Even if I only barely know what "rank" and "p-class" are, 2045 on that list stands out. Is there any other way to describe it? For example, is it the Sylow subgroup of any simple group?