(C₃⋊D₃)⋊D₁₁ #87691

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

Aliases

unambiguous semidirect product	(C₃⋊D₃)⋊D₁₁
unambiguous semidirect product	D₃₃⋊D₃

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

44 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 66

A minimal faithful permutation representation — 2 generators on 17 points:

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

Polycyclic presentation:

2^2,3^2,11|c^a=c^2,e^a=e^10,c^b=c^2,d^b=d^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 23);