C₂×C₇×C₈ #1149

order	112
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂²×C₃×D₄ (order 96) · Inn(G) = C₁ · Out(G) = C₂²×C₃×D₄
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₇×C₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(112, 22);