C₉×C₂²⋊D₇ #92602

order	504
isoclinism	isoclinic class of Dic₁₄
automorphism	Aut(G) = C₂³×C₃×AGL(1,𝔽₇) (order 1008) · Inn(G) = C₂×D₇ · Out(G) = C₂²×C₃²
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 252

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,4,6,7,5,3)(9,11)(12,13,15,14,16,18,17,19,20);(2,3)(4,5)(6,7)(8,9)(10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(504, 28);