C₄²×Q₁₆ #20499

order	256
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) order 196608
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₄²×Q₁₆

555 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4);(5,6,7,8);(9,10,11,12,13,14,15,16)(17,24,23,22,21,20,19,18);(9,17,13,21)(10,18,14,22)(11,19,15,23)(12,20,16,24)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13487);