C₂×C₄×Dic₉ #63484

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

Aliases

direct product	C₂×C₄×Dic₉
unambiguous semidirect product	(C₂×C₉)⋊C₄²

C₉ ⋊ C₂×C₄²

162 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 132);