C₂²×C₁₇ #597

order	68
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = D₃×C₁₆ (order 96) · Inn(G) = C₁ · Out(G) = D₃×C₁₆
holomorph	G ⋊ Aut(G) = S₄×AGL(1,𝔽₁₇)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₇

10 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 68

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(68, 5);