C₂²×C₄₇ #4423

order	188
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×D₃×C₂₃ (order 276) · Inn(G) = C₁ · Out(G) = C₂×D₃×C₂₃
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₄₇

10 conjugacy classes of subgroups.

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 188

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(188, 4);