C₃²×#217 #88832

order	432
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂²×C₃

Aliases

C₃³ ⋊ C₂²⋊C₄

332 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 72

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 479);