C₁₆×M₁₆ #11407

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂×#72280587 (order 4096) · Inn(G) = C₂² · Out(G) = C₂×#7629437
homology	Abelianization (H₁) = C₂×C₄×C₁₆ · Schur multiplier (H₂) = C₂×C₄

Aliases

C₁₆×M₁₆

153 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 24 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 4395);