Direct product of A4 and D8

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This group is defined as the external direct product of alternating group:A4 and dihedral group:D8.

Arithmetic functions

Function Value Similar groups Explanation
order (number of elements, equivalently, cardinality or size of underlying set) 96 groups with same order order of direct product is product of orders: the order is thus 12 \times 8 where 12 = 4!/2 is the order of alternating group:A4 and 8 is the order of dihedral group:D8.
exponent of a group 12 groups with same order and exponent of a group | groups with same exponent of a group exponent of direct product is lcm of exponents: we get \operatorname{lcm} \{ 6,4 \} = 12.
derived length 2 groups with same order and derived length | groups with same derived length derived length of direct product is maximum of derived lengths: we get \max \{ 2,2 \} = 2.

GAP implementation

Group ID

This finite group has order 96 and has ID 197 among the groups of order 96 in GAP's SmallGroup library. For context, there are 231 groups of order 96. It can thus be defined using GAP's SmallGroup function as:



gap> G := SmallGroup(96,197);


IdGroup(G) = [96,197]

or just do:



Other descriptions

Description Functions used
DirectProduct(AlternatingGroup(4),DihedralGroup(8)) DirectProduct, AlternatingGroup, DihedralGroup