C₃⋊(C₃⋊#261) #90863

order	468
isoclinism	isoclinic class of C₃⋊(C₃⋊#261)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₃	C₄
prime radical, cosocle	C₃²×D₁₃	C₂
LCS	G ▷ C₃²×C₁₃
UCS	C₁

36 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:

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

Polycyclic presentation:

2^2,3^2,13|a^2=b,c^a=c^2,d^a=d^2,e^a=e^5,e^b=e^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 38);