C₂²×C₄₃ #4302

order	172
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×D₃×C₇ (order 252) · Inn(G) = C₁ · Out(G) = C₂×C₃×D₃×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₄₃

10 conjugacy classes of subgroups.

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 172

A minimal faithful permutation representation — 2 generators on 47 points:

(1,2)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(3,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(172, 4);