C₉×Dic₇ #6965

order	252
isoclinism	isoclinic class of D₇
automorphism	Aut(G) = C₂²×C₃×AGL(1,𝔽₇) (order 504) · Inn(G) = D₇ · Out(G) = C₂²×C₃²
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

derived, Sylow	C₇ ⋊ C₄×C₉
Hall	C₇×C₉ ⋊ C₄

18 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(252, 4);