C₄²×D₉ #63433

order	288
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄²×D₉

Fitting	C₄²×C₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₄²

162 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 81);