order	396
isoclinism	isoclinic class of C₃⋊D₃×D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃⋊D₃×D₁₁
unambiguous semidirect product	(C₃×D₁₁)⋊D₃

Splittings

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁	C₂²
LCS	G ▷ C₃²×C₁₁
UCS	C₁

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 99

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 20);