C₄²×C₂²⋊C₄ #13747

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) order 3145728
homology	Abelianization (H₁) = C₂×C₄³ · Schur multiplier (H₂) = C₂⁴×C₄³

Aliases

direct product	C₄²×C₂²⋊C₄
unambiguous semidirect product	C₂²⋊C₄³

1671 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 16 points:

(1,2,3,4);(5,6,7,8);(9,10)(11,12)(13,14,15,16);(10,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6735);