C₃²×Dic₃⋊C₄ #88825

order	432
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃²×Dic₃⋊C₄
unambiguous semidirect product	Dic₃⋊(C₃²×C₄)

C₃³ ⋊ C₄⋊C₄

220 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 472);