C₂×C₁₁² #6853

order	242
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₅×#72210865 (order 13200) · Inn(G) = C₁ · Out(G) = C₅×#72210865
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁₁

Aliases

C₂×C₁₁²

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 242

A minimal faithful permutation representation — 2 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)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(242, 5);