Function 
Value 
Similar groups 
Explanation for function value

underlying prime of pgroup 
{{{underlying prime}}} 


order (number of elements, equivalently, cardinality or size of underlying set) 
{{{order}}} 
groups with same order "{{{order}}}" is not a number. 

primebase logarithm of order 
{{{order plog}}} 
groups with same primebase logarithm of order "{{{order plog}}}" is not a number. 

maxlength of a group 
{{{order plog}}} 

maxlength of a group equals primebase logarithm of order for group of prime power order

chief length 
{{{order plog}}} 

chief length equals primebase logarithm of order for group of prime power order

composition length 
{{{order plog}}} 

composition length equals primebase logarithm of order for group of prime power order

exponent of a group 
{{{exponent}}} 
groups with same order and exponent of a group "{{{exponent}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and exponent of a group "{{{exponent}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same exponent of a group"{{{exponent}}}" is not a number. 

primebase logarithm of exponent 
{{{exponent plog}}} 
groups with same order and primebase logarithm of exponent "{{{exponent plog}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and primebase logarithm of exponent "{{{exponent plog}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same primebase logarithm of exponent"{{{exponent plog}}}" is not a number. 

Frattini length 
{{{exponent plog}}} 
groups with same order and Frattini length "{{{exponent plog}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and Frattini length "{{{exponent plog}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same Frattini length"{{{exponent plog}}}" is not a number. 
Frattini length equals primebase logarithm of exponent for abelian group of prime power order

minimum size of generating set 
{{{rank}}} 
groups with same order and minimum size of generating set "{{{rank}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and minimum size of generating set "{{{rank}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same minimum size of generating set"{{{rank}}}" is not a number. 

subgroup rank of a group 
{{{rank}}} 
groups with same order and subgroup rank of a group "{{{rank}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and subgroup rank of a group "{{{rank}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same subgroup rank of a group"{{{rank}}}" is not a number. 
same as minimum size of generating set since it is an abelian group of prime power order

rank of a pgroup 
{{{rank}}} 
groups with same order and rank of a pgroup "{{{rank}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and rank of a pgroup "{{{rank}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same rank of a pgroup"{{{rank}}}" is not a number. 
same as minimum size of generating set since it is an abelian group of prime power order

normal rank of a pgroup 
{{{rank}}} 
groups with same order and normal rank of a pgroup "{{{rank}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and normal rank of a pgroup "{{{rank}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same normal rank of a pgroup"{{{rank}}}" is not a number. 
same as minimum size of generating set since it is an abelian group of prime power order

characteristic rank of a pgroup 
{{{rank}}} 
groups with same order and characteristic rank of a pgroup "{{{rank}}}" is not a number.
 "{{{order}}}" is not a number.
 groups with same primebase logarithm of order and characteristic rank of a pgroup "{{{rank}}}" is not a number.
 "{{{order plog}}}" is not a number.
 groups with same characteristic rank of a pgroup"{{{rank}}}" is not a number. 
same as minimum size of generating set since it is an abelian group of prime power order

nilpotency class 
1 

The group is a nontrivial abelian group

derived length 
1 

The group is a nontrivial abelian group

Fitting length 
1 

The group is a nontrivial abelian group
