order	414
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃⋊D₃×C₂₃
unambiguous semidirect product	C₃⋊(D₃×C₂₃)

Splittings

Fitting, socle, Hall	C₃²×C₂₃ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₂₃

	subgroup	G/H
center, hypercenter	C₂₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₂₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂₃

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 207

A minimal faithful permutation representation — 3 generators on 29 points:

(2,3)(5,6)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29);(4,5,6);(1,2,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(414, 8);