C₂²×C₇ #87

order	28
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃×D₃ (order 36) · Inn(G) = C₁ · Out(G) = C₂×C₃×D₃
holomorph	G ⋊ Aut(G) = S₄×AGL(1,𝔽₇)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₇

10 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 28

A minimal faithful permutation representation — 2 generators on 11 points:

(1,2)(5,6,7,8,9,10,11);(3,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28, 4);