C₄²×C₅²⋊C₃ #11925165

order	1200
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₄×C₅

Aliases

C₄²×C₅²⋊C₃

Fitting, Hall	C₄²×C₅² ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₄²

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4)(9,10,12)(11,15,17)(13,18,21)(14,20,23)(16,19,22);(5,6,7,8)(9,11,16,21,23)(10,15,19,13,14)(12,18,17,20,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 375);