C₁₁⋊#157 #87686

order	396
isoclinism	isoclinic class of C₁₁⋊#157
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₁	C₄
prime radical, cosocle	C₁₁×C₃⋊D₃	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁

20 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)(3,4,6,5)(8,9)(10,11)(12,13)(14,15)(16,17);(1,3,6)(7,8,10,12,14,16,17,15,13,11,9)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(396, 18);