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

Aliases

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

Splittings

Fitting, socle, Hall	C₃²×C₁₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₁₉

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₉

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 171

A minimal faithful permutation representation — 3 generators on 25 points:

(2,3)(5,6)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25);(4,5,6);(1,2,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(342, 16);