C₅²×Dic₃ #64475

order	300
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×Dic₃
unambiguous semidirect product	C₃⋊(C₄×C₅²)

derived, Sylow	C₃ ⋊ C₄×C₅²
Hall	C₃×C₅² ⋊ C₄

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 300

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 18);