16Gamma2c

Definition

The lattice of normal subgroups with families indicated

It is member $c$ of the Hall-Senior family $\Gamma _{2}$ for groups of order $16$.

Members

There are two members:

Member name	Hall-Senior symbol	Second part of GAP ID	Hall-Senior number
SmallGroup(16,3)	$16\Gamma _{2}c_{1}$	3	9
SmallGroup(16,4)	$16\Gamma _{2}c_{2}$	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.