order	468
isoclinism	isoclinic class of C₃⋊D₃×D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃⋊D₃×D₁₃
unambiguous semidirect product	(C₃×D₁₃)⋊D₃

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 117

A minimal faithful permutation representation — 3 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 43);