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Template:Particular Hall-Senior genus


The lattice of normal subgroups with families indicated


It is member c of the Hall-Senior family \Gamma_2 for groups of order 16.


There are two members:

Member name Hall-Senior symbol Second part of GAP ID Hall-Senior number
SmallGroup(16,3) 16\Gamma_2c_1 3 9
SmallGroup(16,4) 16\Gamma_2c_2 4 10

Arithmetic functions

Arithmetic functions with unambiguous values by definition of genus

These are arithmetic functions whose values are unambiguous by the definition of Hall-Senior genus for groups of a given order.

Function Value Explanation
order 16
prime-base logarithm of order 4
nilpotency class 2
derived length 2
Frattini length 2
prime-base logarithm of order of inner automorphism group 2
prime-base logarithm of order of derived subgroup 3

Arithmetic function values for both members

Note that some of these arithmetic function values are the same for both members, but this is true only because of the particular genus.