C₄²×C₃⋊D₃ #64080

order	288
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₃×C₄

Aliases

C₄²×C₃⋊D₃

Fitting	C₃²×C₄² ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₄²

324 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 728);