order	342
isoclinism	isoclinic class of D₃×C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₉⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₁₉⋊C₃)
unambiguous semidirect product	(D₃×C₁₉)⋊C₃

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 57

A minimal faithful permutation representation — 2 generators on 22 points:

(2,3)(5,6,8)(7,10,11)(9,13,12)(14,18,16)(15,19,17)(20,22,21);(1,2,3)(4,5,7,11,16,21,18,6,9,14,19,8,12,17,10,15,20,22,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(342, 10);