C₃²×C₄⋊Dic₃ #88826

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

Aliases

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 473);